Home

Mapping Toolbox User's Guide

Contents

1. 00000 6 27 Plotting Patches 0 cece tee 6 27 Changing the Stacking Order of Mapped Objects 6 28 Hiding the Mouse Buttons 0 0c e eee eee 6 29 Toggling the Map GridandFrameOn 6 30 Constructing Personalized Map Data with GUIs 6 31 Trimming an Existing Data Set 0055 6 31 Encoding a Regular Surface Map 00 cee eee eee 6 33 Creating a Personalized Colormap 0 00 6 41 External Data Interface 7 A Working With External Data 7 2 Global Vector Data 2 0 cece eee 7 3 The Digital Chart of the World 200 cee ee eae 7 3 Looking Up Names and Locations in the DCW Gazetteer 7 3 Importing DCW Themes 0 0000 cee eee ee 7 5 Reading DCW Files Directly 00000 00a 7 13 U S Vector Data 002s 7 14 TIGER LINE sacs can choke chen ce ia we Np EES a imi 7 14 TIGER Thinned Boundary 00 eee eens 7 18 TIGER Arclnfo Format 0 cc cece eee eee 7 18 TIGER MapInfo Interchange Format 7 21 Global Gridded Elevation Data 7 23 ETOPOS5 and TerrainBase 00 e eee eee 7 23 Digital Chart of the World DEMS 00 00005 7 28 U S Gridded Elevation Data 00 0c eee eee 7 32 Astronomical Data 0 0 cece eee 7 36 Geographic Terms
2. 2 43 Interacting with Displayed Maps 2 47 Specialized Map Displays 2 055 2 50 Thematic Map Functions 00 0c eee eee eee 2 50 Choropleth Maps 000s cece eee tee tte eee 2 52 2 Displaying Maps Introduction to Mapping Graphics One of the fundamental concepts underlying the Mapping Toolbox is the idea that maps are variables that exist independently of their display H owever for visual geographic data analysis application development and presentation of results quality display capabilities are a must With the Mapping Toolbox you can display geographic information almost as easily as you can plot regular data in MATLAB Most mapping commands are similar to MATLAB commands except they deal with latitude and longitude spherical coordinates instead of x and y Cartesian coordinates Mapping commands typically havethe same names as their MATLAB counterparts with the addition of an m for maps at the end F or example the Mapping T ool box analog to MATLAB s pl ot command is pl otm The Mapping Toolbox manages most of the steps in displaying a map It will project your data cut and trim it to desired limits and display the resulting map for you The toolbox also provides the means to add other elements to your displayed map such as a frame gridlines coordinate labels and text labels If you change your projection properties or even the projection itself
3. Of course few projections are actually true cylindrical projections but the concept of the wrapped cylinder is nonetheless a convenient way tothink about it Perhaps the best way to gain an appreciation for projection aspect is to look at a few examples NOTE The projection aspect discussed in this section is different from the map axes Aspect property The map axes As pect property controls the orientation of the figure axes For instance if a map isin a normal setting witha landscape orientation a switch toa transverse aspect rotates the axes by 90 resulting in a portrait orientation The projection aspect deals with the display orientation of the map projection One cannot change the projection aspect by simply altering theAs pect property the Ori gi n vector must be used instead Here a psuedocylindrical projection the Sinusoidal is used First look at the normal aspect of this projection Normal Aspect Origin at 0 0 Orientation 0 origin vector 0 0 OJ In the normal aspect the North Pole is at the top of the image To create a transverse aspect imagine pulling the North Pole down to the center of the image which was originally occupied by the point 0 0 4 10 Projection Aspect The shape of the frame is unaffected this is still a Sinusoidal projection Transverse Aspect Origin at 90 N 0 Orientation 0 origin vector 90 0 OJ The
4. framem gridm mlabel plabel displ aym POI ine displ aym PPpoi nt displ aym PPtext W orld Vector Data The zoomed in region of Europe allows the names of the major cities to be read more easily NOTE Unlike vector and matrix data text objects are not automatically trimmed when they fall outside the map frame limits You can remove them later using a graphics program or write a script or function that removes them for you There are other ways to represent political data We can display the countries as patches label them with strings from the 0t ext structure and pick random colors for the patch faces Clear the previous line map and redraw the patch map cl ma displ aym POpatch displ aym POt ext colormap rand 200 3 3 Atlas Data 3 8 Here is the result Note how the separated parts of countries are filled with the same colors Sardinia and Sicily for example are shaded the same color as the boot of Italy This is accomplished automatically because each of the components is tagged as Italy Every element in a wor dio structure has a tag field Drainage data has been tagged to distinguish between rivers and lakes The political ocean lines are tagged as coastlines or international boundaries and the political patches have been tagged with the names of the country Both of the functions di sp ay m and ml ayers usethesame colors for similarly tagged objects if noot h
5. PPpatch PPtext dcwdata cdrom NOAMER 41 44 72 69 PP patch text setm gca MapLatLimit 41 13 42 75 MapLonLimit 71 7 69 8 hPPpatch displ aym PPpatch set hPPpatch FaceColor y hPPtext displaym PPtext set hPPtext Font Size 6 71 W 70 W 42 Vineyard Ye Narag e NFABRT y Jap T Wi West Tisbury 7 12 G lobal Vector Data There is more data describing man made features including airports railroads utilities cultural landmarks and transportation structure The DCW also contains data for the natural world The drainage and elevation contours are perhaps the most extensive data themes Hereis a map of the drainage and contour data Reading DCW Files Directly The high level dcwdat a function is the most convenient way to read data from the DCW because it integrates information from many different files in different directories Individual DCW files are less useful because few of them contain completeinformation Most people will have little need to read the raw DCW data files If you need todo so the Mapping Toolbox can read most DCW files into MATLAB structures using thedcwread function The External Data Reference section of the Mapping Toolbox Reference Guide has more information on directly accessing individual DCW files Moreinformation on the relationships between thefiles and the meaning of the data in the files can be found in the Mi
6. What can we say about their homes relative to yours dist2tuls distance midl_lat midl_lon tuls_lat tuls_lon dist2tuls 6 5032 dist2newo distance midl_lat midl_lon newo_lat newo_lon dist2newo 10 4727 Tulsa is about 6 5 degrees distant New Orleans about 10 5 degrees distant The great circle azimuths are the following az2tuls azimuth midl_lat mid _lon tuls_lat tuls_lon az2tuls 48 1386 az2neworl azimuth mid _lat midl_l on newo_lat newo_lon az2neworl 97 8644 The absolute difference in these azimuths is 49 7258 a fact we will use later Today you feel on top of the world so make Midland Texas the north pole of a transformed coordinate system To do this first determine the origin required to put Midland at the pole origin newpole mid _lat midl_lon origin 58 78 0 4 15 4 M ap Projections The origin of the new coordinate system will be 58 N 78 E Midland is now at a new latitude of 90 What are the new coordinates of Tulsa and New Orleans Tocalculate these use ther ot at em command Since it defaults to radians be sure to include the units input degrees tuls_lati tuls_lonl rotatem tuls_lat tuls_lon origin forward degrees tuls_latl 83 4968 tuls_lonl 48 1386 newo_latl newo_lonl rotatem newo_lat newo_lon origin forward degrees newo_latl 19 5273 newo_lonl 97 8644 Now test the new coordinate syste
7. 0c cee eee 1 10 Measuring Azimuth 0 00 c eee eee 1 11 Reckoning Positions 0 00 eee eee 1 13 Small ht fa e en Re eae cee eee eee a E oe are 1 13 Measuring Area 2 cee 1 15 The Geoid Model 0 20 cee eee 1 16 What IS a Geoid 0 0 a 1 16 The Geoid Vetor 6 eee 1 17 What Is the Correct Geoid Vector 5 1 18 Measuring the Planets 000 e eee eee 1 19 v Contents Angles Times and Distances Units and Notation 1 21 Angular Notation oro evden way eae a aA 1 21 Peg oes nyy aaraa be ee ee ese Ua Sid wean eee 1 21 RAGIANS s p24 ahaa 24 wok ia a ea ee adda toate 1 21 Degrees Minutes Seconds 00 cece eee eee 1 21 Converting Between Angle Unit Formats 1 22 Time Notation s s s anaana nananana 1 23 FOURS a Gaiaren e aaae n eA Rei ae Oe A E a wa i a 1 23 SCCOMAS Hastie Ree E TAA URE DE aca eee k Soe ARNT ad Soa 1 23 Hours Minutes Seconds 0 0c eee eee eee 1 23 Converting Between Time Unit Formats 1 24 Distance Notation 0 0 c cece ee 1 24 Working with Vector Maps 5 1 25 Data Formats Pereas tiar tee aes Ee hed eka Se ees 1 25 Segments versus Polygons 00 c cece eee eee 1 26 Creating Vector Data ce ees 1 27 Calculating Small Circles 0 0 02 0ca eee ee 1 27 Calculating Tracks Great Circles and Rhumb Lines 1 28 Geograp
8. 30 45 MapLonLimit 115 135 meshm map maplegend size map map demcmap map lightm 37 5 125 Position 1 0 1 material 5 5 1 lighting phong set gca DataAspectRatio 1 1 50000 view 0 75 2 41 2 Displaying Maps The light effects employed here are different and separate from those used by surfm meshisrm andsurflsrm Here alight object is added directly tothe map surface Like all displayed surfaces the light object is a separate MATLAB graphic object with its own object handle For the functions mesh sr m and surflsrm light effects are simulated within the functions by modifying the colormap with bands of light and dark The map matrix is then converted to indices for the new shaded colormap based on calculated surface normals Using light objects allows for a wide range of different light effects such as ambient light light color and surface reflectance properties but will ultimately require more memory and time to display The meshl sr mand surf l srm functions provide a simple means of displaying maps with simulated light effects Both shaded relief formats represent the best available method of displaying matrix maps since both large surface coloring and small Surface shading features can be examined on one map For more information consult the reference pages for mes hl srm surflsrm and i ght min the Mapping Toolbox Reference Guide along with the section on lighting in the MA
9. Enter citylats andcitylons as the latitude and longitude variables In the Other Properties edit box type Font Size 9 and press Apply The city labels will appear on the map The Complete GUI Environment maptool Hereis the result SSS H Figure No 1 For more information on using GUIs to plot text objects see the GUI Reference section of the Mapping Toolbox Reference Guide Editing Text Position The properties of many mapped objects can be edited with the Click and Drag Property Editor tool Pressing the Alt key and clicking on the object activates this functionality and allows for property manipulation through simple mouse clicks and drags To move a city label away from its marker a bit press the alt key and click on the text A Click and Drag Property Editor box for text objects appears text Color ab2 Alignment left Fonthame ab2 FontSize ab2 Drag Edit 6 15 6 G UI Tools 6 16 Click Drag and the label will now follow the mouse pointer as it is moved across the map display Position the label where you like and click to place the text All the labels can be repositioned using the Click and Drag Property Editor B E Figure Na 0 Saar For more information on using the Click and Drag Property Editor tool see the GUI Reference section of the M apping Toolbox Reference Guide
10. MapLatLimit 30 60 MapLonLimit 15 45 MapParallels Theaxesm function will automatically set the origin and frame limits for a map centered on the limited geographic region with the results of subsequent mapping display commands shown only within the specified limits Empty matrices are used to force recalculation of a property or a return to the default value For example setting the map parallels to an empty matrix will automatically determine map parallels appropriate for the current map limits minimizing distortion in the projection Since the MapProj ection property is the only property that must be explicitly set it can be specified without the property name as long as the projection name is the first argument in axes m For instance axesm miller PropertyNamel PropertyValuel PropertyName2 PropertyValue2 Theaxesm command without any arguments activates a GUI that allows for easy manipulation of the map axes properties 2 4 Map Axes For proper map appearance and ease of use the Mapping Toolbox changes some of the default MATLAB axes properties The altered properties are e TheNext Plot property issetto add e TheUser Data property contains the map projection structure that defines the specific map axes properties e TheBox property is set to on e TheBut t onDownFcn property is set tothe function ui mapt bx which processes callbacks for Mapping Toolbox objects e Thecomman
11. Thesimplest way to display a matrix map is to assign colors to matrix elements according to the value of their data The map can be displayed either as a 2 D image or a 3 D surface using the map values as the z data Consider the matrix map located in thek or ea workspace It contains a matrix of land elevations and bathymetry data for the region around the Korean peninsula along with a map legend variable which indicates a regular matrix map format Calculate a graticule for the regular matrix map using the meshgrat function sothat a general matrix map is also available Also convert the units for the map matrix from meters to degrees so they are consistent with the latitude and longitude coordinate matrices load korea lat lon meshgrat map mapl egend map km2deg map 1000 whos Name Size Bytes Class lat 180x240 345600 double array lon 180x240 345600 double array map 180x240 345600 double array mapl egend 1x3 24 double array Noticethat the at and on coordinate matrices or graticule arethe same size as the map matrix a requirement for constructing 3 D surfaces You have already seen the mes hm command used to display regular matrix maps so display the korea matrix map using thes ur f m command axesm MapProjection eqaconic MapParallels MapLatLimit 30 45 MapLonLimit 115 135 surfm lat lon map map demcmap map set gca DataAspectRatio 1 1 5 view 0 75 2 36 Displaying M atrix
12. figure axesm trystan displaym state 2 45 2 Displaying Maps Here is the map in a Trystan Edwards Cylindrical projection Fig gt You can also treat geographic data structures as databases of map data The extract m function lets you retrieve data from the formatted structure F or example you can extract the state of Massachussetts from thes t at e structure lat long extractm state mass NOTE Most of the Mapping Toolbox atlas data and data from public sources processed by Mapping Toolbox external interface functions enters the MATLAB workspace as geographic data structures You can also format your own data as geographic data structures 2 46 Interacting with Displayed M aps Interacting with Displayed Maps The Mapping Toolbox provides the means to interact with displayed maps The input m command allows you to get the latitude longitude position of a mouse click the gc pmap function returns the current mouse position again in latitude and longitude As an example display a map axes with its grid The lines of code below allow you to click on the map three times and store the geographic coordinates for the three points selectedin at and ong The final pl ot m command will plot the points you clicked on The display shown here corresponds to the points chosen for the example axesm sinusoid framem on gridm on points input m 3 points 28 9373 62 1631 1 1575 149 3467 67
13. have a fixed set An axes s MapProjection property does not of property values setm gca Frame Frame on off setm gca FixedOrient FixedOri ent FixedOrient is a read only property 2 10 The Map Frame The Map Frame In the Mapping Toolbox the map frame is a box enclosing the geographic display The frame is displayed if the map axes property Frame is set to on This can be accomplished upon map axes creation with axes m with set m or with the direct command framem on The frame is geographically defined as a latitude longitude quadrangle that is projected appropriately For example on a map of the world the frame might extend from pole to pole and a full 360 in longitude In appearance the frame would take on the characteristic shape of the projection The examples below are full world frames shown in three very different projections Full World Map Frames Equidistant Cylindrical Sinusoidal Projection Projection Robinson Projection 2 11 2 Displaying Maps As a map object each of the previously displayed frames is identical however the selection of a display projection has varied their appearance Since each of the examples shows the entire world FLat Limit iS 90 90 andFLonLi mit is 180 180 for each case The frame quadrangle can encompass smaller regions as well Frame Quadrangles Shown in the Robinson Projection Symmetric about Prime Meridian Lat 30
14. hms format for example two times in this format cannot simply be added It is advisable to convert hms data to decimal hours before working extensively with it 1 23 I apping Fundamentals Converting Between Time Unit Formats Time units can be converted using functions similar to those described for angle unit conversions Theseincludehr2sec andhms 2hr as well as a general conversion function t i medi m which works just likeangl edi m Distance Notation Distances in the Mapping Toolbox can be measured in a number of different units Functions are provided to convert between nautical miles nm statute miles sm kilometers km degrees of arc length deg and radians of arc length rad The names of these functions are of the forms m2k m km2rad etc A general distance conversion function dist dim is available as well There is no single default unit of distance measurement in the toolbox Navigation functions use nautical miles as a default almanac functions default to kilometers and thedi st ance function defaults to degrees of arclength It is essential that you understand the default units of any function you use NOTE When distances are given in terms of angular units degrees or radians be careful to remember that these arein terms of arclength Whilea degree of latitude always subtends a degree of arc length this is not necessarily the case for degrees of longitude Also using arclength as d
15. 1 axesm mercator meshm map mapl egend size map map demcmap map lightm 18 25 66 275 material 7 7 1 5 lighting gouraud 7 30 Global Gridded Elevation Data The increase in resolution over the ETOPO5 and TerrainBase datasets can be appreciated from a map of the Cape Cod region The 30 arc second DCW DEM data covers this region with a 360 by 360 matrix which is 10 times finer than the 5 arc minute 300 arc second ETOPO5 and TerrainBase data This is also the same resolution as the data in the MATLAB cape workspace map maplegend dcwdem na_30_dem3 1 41 44 72 69 map isnan map 1 whos Name Size Bytes Class ma p 360x360 1036800 double array mapl egend 1x3 24 double array axesm MapProjection mercator MapLatLimit 41 44 MapLonLimit 72 69 framem gridm MLineLocation 1 Plinelocation 1 ml abel MLabelLocation 1 plabel PLabelLocation 1 meshm map mapl egend demcmap map 69 W 42 av 7 31 7 External Data Interface U S Gridded Elevation Data The highest resolution digital elevation maps accessible through the M apping Toolbox external interface functions cover most of the United States at a horizontal resolution of about 100 meters They are distributed by the U S Geological Survey as separate 1 degree quadrangles covering the contiguous United States Hawaii and limited portions of Alaska The 1 degree DE Ms are also referred to as 3
16. 2 7358 0 1321 1 22 Angles Times and Distances Units and N otation Similar functions includedeg2rad rad2deg deg2dms etc Thereis also a more general function ang edi m which will convert from one format to another F or example how many degrees arein radians degs angledim1 4 pi radians degrees degs 45 Time Notation Times can be represented as variables in the Mapping Toolbox in three ways hours seconds and hours minutes seconds The toolbox provides functions for converting between these formats Hours This is the default time unit notation for the toolbox Hour notation is simply decimal notation in terms of hours Two hours and fifteen minutes would be 2 25 Seconds Seconds notation is simply decimal notation in terms of seconds One hour would be 3600 Hours Minutes Seconds H ours minutes seconds or hms notation is analogous to dms notation for angles In text an hms time would be hh mm ss F or example 12 36 15 is 12 hours 36 minutes and 15 seconds In the Mapping Toolbox when hms times are represented by a single number the format is hhmm ss F or example 12 36 15 is 1236 15 The real value of this notation is in entering data already in this format The toolbox includes the mat 2hms function to easily input hms data which functions very similarly tothe mat 2dms function described earlier NOTE Care must be exercised when working with the
17. 3 21 3 Atlas Data Finally look at the region around Cape Cod again to get an impression of the detail of the data figure axesm MapProjection mercator Frame on MapLatLimit 41 44 MapLonLimit 72 69 gridm MLineLocation 1 PLineLocation 1 GLineStyle ml abel MLabel Location 1 plabel PLabel Location 1 displaym state colormap summer 43 42 41 Thereis an obvious compromise between the size of a dataset and its accuracy and detail This data can be displayed relatively quickly for displays of all the United States but it is not suitable for mapping smaller regions Note the generalized character of the coastline and the absence of small islands M ore detailed and accurate data is availablein theusahi workspace and through the Mapping Toolbox External Data Interface functions 3 22 United States Vector Data Medium Resolution State Outlines Another more detailed set of state outlines is available in the M apping Toolbox The data in theusahi MAT fileis similar in format tothest ate structure found in usal o but contains more detailed coastlines and islands The resolution of statel ine intheusahi workspace is about three times greater than the corresponding st ate in theusalo workspace load usahi whos Name Size Bytes Class statelin 1x51 837656 Struct array statepatch 1x51 837758 Struct array statetext 1x51 51190 struct array The listed variable
18. However unlike MATLAB lighted surfaces that do not modify the surface s CDat a these mapping commands construct a new colormap and associated CData matrix by using grayscales to lighten or darken a matrix component based on its calculated surface normal to a light source To display a lighted shaded relief map type the following cl ma surflsrm lat on map 2 39 2 Displaying Maps 2 40 Mapped Light Objects The Mapping Toolbox allows for the mapping of light objects using the i ght m command which is similar tothe i ght command in MATLAB Here placea lighted source at an infinite distance representing the Sun at the summer solstice 23 5 N at local apparent noon in Natick Massachusetts 71 W load topo ptopo topo ptopo topo lt 0 0 ptopo 100 ptopo almanac earth radius 1000 axesm globe view 15 38 meshm topo topolegend size topo ptopo demcmap topo shading interp lightm 23 5 71 Color y material 5 7 1 5 lighting phong Thetopo surface had been modified to show the 3 D features of land only which is vertically exaggerated by a factor of 100 The ocean depths are shown by color only Displaying M atrix Maps Asa comparison tothe lighted shaded relief example shown earlier add a light source to the surface colored matrix map of the K orean peninsula region shown earlier figure load korea axesm MapProjection eqaconic MapParallels MapLatLimit
19. In this tutorial you may have noticed the use of the function de mc map in several digital elevation map DEM or topographic display examples This function creates colormaps appropriate for the display of DEMs although it is certainly not limited to just DE Ms The colormaps by default have atlas like colors varying with elevation or depth that properly preserve the land sea interface The de mc map function can also be used to create colormaps very different from the default atlas colors Suppose you want to display thet opo map using 16 total colors coloring the oceans a uniform light cyan and the land similar to MATLAB s hsv colormap load topo landclr 00 1 010 10 0 axesm robinson meshm topo topol egend demcmap topo 16 7 1 1 landclr Displaying M atrix Maps Instead of specifying the size of the colormap you can make all values within an elevation band the same color Modify the colormap to use a surface data interval of 100 coloring all land areas black and using the default sea colors to take a closer look at the bathymetry data demcmap inc topo 100 0 0 0 Usethestring inc asthe first input argument to indicate that a desired elevation interval or increment is to be used to build the colormap Y ou can also employ the default colors for the sea by entering an empty matrix in place of an RGB color vector 2 35 2 Displaying Maps Data Representation Image and Surface Coloring
20. 60 L 80 100 L 1 L L f 200 150 100 50 0 50 100 150 200 What happened Recall that the original data extended beyond 180 longitude In the projection transformation process longitude data outside 180 180 degrees is projected back into this range since angles differing by 360 are geographically equivalent The data from the inverse transformation process therefore jumps from 180 to 180 as depicted by the straight horizontal lines in the figure above 4 21 4 Map Projections Summary Guide Literally an infinite number of possible map projections can be constructed The Mapping Toolbox provides 60 different map projections To view all the projections in the toolbox use the command maps Cartographers choose a map projection by determining which property distortions they want to minimize or eliminate if any They also determine which of the three projection types cylindrical conic or azimuthal best suits their purpose or they may decide upon special desired features such as straight rhumb lines or great circles true direction or some other interesting trait The following table lists the available projections along with their properties Detailed information on all map projections provided by the Mapping Toolbox can be found in the Mapping T ool box Reference Guide under Projections Reference v g Tegi ee g T E amp os E I 53 5 o Projection Syntax Type g 8
21. 69 The Geographic Meaning A matrix map and its associated map legend can provide a host of geographic information regarding the map and its entries First as was just demonstrated the north south east and west limits of the mapped area can be determined as follows load russia latlim onglim i mitm map map egend latlim 35 80 longlim 15 190 W orking with M atrix Maps The map in ther ussi a workspace extends over the International Date Line 180 longitude You could use the previously described command npi 2pi to rename the eastern limit to be 170 or 170 W 150 E 180 E 30 E 60 E 90 E 120 E The command set t n allows you to determine the geographic coordinates of a particular matrix element Thereturned coordinates actually show the center of the geographic area represented by the matrix entry row 23 col 79 lat long setIltIln map mapl egend row col lat 39 5000 long 30 7000 You can also determine the row and column of the matrix map entry containing a given point r c setpostn map maplegend lat l ong f 23 79 1 45 I apping Fundamentals 1 46 Each matrix entry can be thought of as an angular square which includes its northern and eastern edges but not its western and southern edges N These edges included n A Matrix Map Entry These edges excluded The exceptions to this are that the southernmost row row 1 also c
22. 90 120 150 180 60 30 Notice that only 9 of the 16 total cells are displayed The value displayed for each cell is the value at the upper left corner of that cell whose coordinates are given by the corresponding at andi ong elements By MATLAB convention thelast row and column of the map matrix is not displayed although they exist in theCData property of the surface object For the second interpretation consider a 3 by 3 map matrix with the same at and ong variables map 1 2 3 45 6 7 8 9 1 57 I apping Fundamentals 1 58 Here is a surface plot of the map matrix with the values of map shown at the center of the associated cells g 80 150 120 90 60 30 O 30 60 90 120 150 180 60 430 All of the map data is displayed for this general matrix map The value of each cell is the value at the center of the cell and the latitudes and longitudes in the coordinate matrices are the boundaries for the cells You may have noticed that the first row of the matrix is displayed as the top of the map whereas for a regular matrix map the opposite was true the first row corresponded to the bottom of the map This difference is due to the at and ong matrices and how they are ordered The at and ong coordinate matrices determine the arrangement of the general matrix map W or
23. Anchorage for example by the following commands indx strmatch Anchorage namestruc name i ndx code namestruc indx id code 2020 Usethetigerp function toread and process Alaska s thinned county boundaries data into Mapping Toolbox geographic data structures 7 19 7 External Data Interface Plot the data in a Lambert Conformal Conic projection COpatch COtext tigerp namestruc co_02_p dat axesm MapProjection lambert MapLatLimit 50 73 MapLonLimit 175 235 MLabel Location 10 MLineLocation 10 PLabelLocation 5 PLineLocation 5 MLabel Parallel south MapParallels framem gridm mlabel pl abel displ aym COpat ch col ormap summer There is one entry in the COpat ch structure for each county with the county name in the tag field TheCOt ext structure contains the text labels for the counties 7 20 U S Vector Data You can also append new data to existing structures or extract only the counties you want The following example reads the county boundaries for Nome and then adds the boundaries for the Aleutians East and Aleutians West to the output structure You can look in thenamestruc structure to find the codes you need COpatch tigerp namestruc co_02_p dat 2180 COpatch tigerp namestruc co_02_p dat COpatch 2013 2016 COpatch 1x3 struct array with fields lat long type otherproperty altitude tag TIGER Mapi
24. Assuming that theEURNAS I A CD is available and mounted on the desktop of a Macintosh computer you can search for the geographic location of the city of Apatin in Yugoslavia by typing dcwgaz EURNASIA apatin APATIN ans type text otherproperty 1x2 cell tag Built up area string APATIN altitude lat 45 6660 long 18 9830 On other computers you must provide a device name as the first argument The string you provide will depend on how the CD ROM is mounted For a Windows PC the command might be dcwgaz F EURNASIA apatin and on a Unix computer with the CD ROM mounted as cdrom you should type dcwgaz cdrom EURNASIA apatin See the documentation that came with your CD ROM drive for more information on how disks are mounted Matches are displayed on screen during thesearch The output is returnedina Mapping Toolbox geographic data structure with the tag identifying the database layer name within the DCW If thereis morethan one entry matching the name the results will be contained in an arrayed structure For example the following command prints to the screen the 95 names in the North American library that begin with the word port and returns the structurestxtstruc andptstruc that can be displayed using displ aym or mlayers txtstruc ptstruc dcwgaz devicename NOAMER port 7 4 Global Vector Data Hereis a map that shows the ports around the G
25. Latitude Limits eg 24 46 Longitude Limits eg D23 181 0 O O To save this trimmed region as vector data choose Customize gt Save As gt Line or Customize gt Save As gt Patch from the menu bar A dialog box will appear prompting you to enter variable names for your new dataset 6 32 Constructing Personalized Map Data with G Uls Themaptrim tool can also be used to convert data from vector format to matrix format To convert the trimmed region around J apan choose Customize gt Save As gt Regular Surface from the menu bar Save the trimmed map data under the variable name map and the map legend under variable name map egend Enter a scale of 5 cells per degree Press OK gt Enter the Surface Map variable names Map Variable map Map Legend Yariable l maplegend Scale cells degree ee Latitude Limits Optional Longitude Limits Optional pS You now havea regular matrix map of J apan in your workspace The Customize Map figure window can now be closed Encoding a Regular Surface Map Encoding is the process of filling in specific values in regions of a matrix map up tospecified boundaries For example you can fill in theinterior of an island bounded by its coastline with the value six Encoding entire regions at one time allows indexed maps to be created quickly A regular matrix map can be encoded using thes eed
26. Plotting Tracks and Calculating Surface Distances To map out your flight plans you can usethetrackui tool Select Display gt T racks from the menu bar The Define Tracks dialog box appears Select Great Circle 2 Point mode To specify Washington D C as the starting point for your first track press the Mouse Select button A crosshair appears on the map display Position it over the city marker and click The coordinates appear in the Starting Point Lat and Lon boxes Using the Ending Point Mouse Select button select London as your ending point The Complete GUI Environment maptool In the Other Properties edit box type Color black LineWidth 2 ZE Define Tracks Style Great Circle Rhumb Line Mode 1 Point 2 Point Angles in degrees Starting Point 39 17 76 86 Ending Point zman J Other Properties Color black LineWidth 2 Press Apply and the first flight track is displayed Now plot the flight from London to Barcelona by again using the mouse to enter those cities as your starting and ending points Press Apply and the second flight track is displayed Now plot your flights back home Use the mouse to specify a track from Venice to Hamburg Todisplay your return flight in a different color changethecolor to green in the Other Properties edit box then press Apply 6 17 6 G UI Tools 6 18 Finally p
27. The DCW contains data for the entire world in separate layers of coverage including political and ocean features drainage hypsography land cover and vegetation populated places roads railroads airports transportation structure and cultural landmarks The features are formatted as patches lines points or text The DCW was published in 1992 on four CD ROMs A new version called VMAPO had been scheduled for release in 1995 but was not available as of early 1997 For more information on purchasing the DCW seethedcwdat a entry in the External Data Reference section of the M appi ng Toolbox Reference Guide The Mapping Toolbox provides high level functions that compile and extract information from the DCW into Mapping Toolbox geographic data structures The following sections introduce these functions and show how to work effectively with the DCW data Looking Up Names and Locations in the DCW Gazetteer One source of information in the Digital Chart of the World is the Gazetteer This is an extensive collection of place names and types within a library The NOAMER library containing the data for North America has 37696 names in its gazette The entire DCW gazette has more than 100 000 names It can be used to quickly find the locations of places and can help to pick the latitude and longitude limits for other DCW functions 7 External Data Interface The Mapping Toolbox interface to the DCW gazette is thedcwgaz function
28. The times at planned positions after the speed change area little earlier the position at the known time 2 a m is a little farther along With this plan you will arrive at the rendezvous about 4 1 2 minutes earlier so you may want to consider a more authoritative speed change Time Zones Early in this manual we gave an example of a time zone calculation The t i mezone function returns a navigational time zone that is one based solely on longitude with no regard for statutory divisions So for example Chicago Illinois lies in the statutory U S Central time zone which has irregular boundaries devised for political or convenience reasons However froma navigational standpoint Chicago s longitude places it in the S Sierra time zone The zone s description is 6 which indicates that 6 hours must be added to local time to get Greenwich or Z Zulu time So if it is noon standard timein Chicago it is 12 6 or 6 p m at Greenwich Navigation Each navigational time zone is 15 of longitude in width and has a distinct description and designating letter The exceptions to this are the two zones on either side of the Date Line M and Y Mike and Yankee These zones are only 7 1 2 wide since on one side of the Date Line the description is 12 and on the other it is 12 Navigational time zones are very important for celestial navigation calculations Although the Mapping Toolbox does no
29. along with further descriptions and documentation TIGER Arcinfo Format The following boundary types are available in the Arcl nfo format state county minor civil division census tract block numbering area American Indian reservation Alaska native village statistical area Alaska native regional corporation urbanized area metropolitan area and congressional district 7 18 U S Vector Data The Arclnfo data files have names ending in p and pa the first represents polygon coordinate data and the latter polygon attributes You will also need the _name dat file or names file containing the FIPS codes and corresponding county names Plot the counties in the state of Alaska as an example You will need the following three files co name dat co_02_p dat and co_02_pa dat F or these files co indicates county boundaries and 02 is the code for Alaska The code 99 is used for files within the continental United States and 15 corresponds to Hawaii Thefiles are compressed in aPC Zip format When extracting make sure the text files are formatted for your computer platform Read all U S county names and FIPS code from the names file There are more than 3000 entries so reading the file may take a while namestruc fipsname co_name dat namestruc 1x3248 struct array with fields name id You can query the FIPS code of a particular city or county in Alaska
30. correspond This is in fact thet opo matrix that is provided in the MATLAB product in the workspace of the same name To display the matrix map type the following cl ma clears map load topo axesm sinusoid meshl srm topo topol egend Thetopo matrix is displayed as a lighted shaded relief map in a Sinusoidal projection Notethat the matrix logic of the map and the projection in which it is displayed arecompletely independent Thet opo variableis a map whether it is displayed or not and it is the same map no matter how it is displayed I apping Fundamentals Composite Maps M any occasions arisein which vector map variables and matrix map variables are used or displayed together For example continental coastlines in vector form might be displayed with matrix temperature data to make the latter more useful When several map variables are used together regardless of type they can be correctly referred to as a single map Since we have our coast andtopo workspaces available from the previous examples we can combine the two in a single map and see how well the two types of data correspond figure axesm robinson meshm topo topolegend demcmap topo plotmlat long r Here is the resulting map Note that the map has been changed from a Sinusoidal to a Robinson projection Essentially we have displayed our matrix map of elevations and dropped the coastal vector data on top of it The red coastal lines fall q
31. difference 301 8962 The azimuths associated with cardinal and intercardinal compass directions are the following North 0 or 360 Northeast 45 East 90 Southeast 135 South 180 Southwest 225 West 270 Northwest 315 Geographic Measurement Reckoning Positions A common problem in geographic applications is the determination of a destination given a starting point an initial azimuth and a distance In the Mapping Toolbox this process is called reckoning A new position may be reckoned in a great circle or a rhumb line sense great circle or rhumb line track As an example an airplane takes off from La Guardia Airport in New York 40 75 N 73 9 W and follows a northwestern rhumb line flight path at 200 knots nautical miles per hour Where would it be after 1 hour rhlat rhlong reckon rh 40 75 73 9 nm2deg 200 315 rhlat 43 1054 rhlong 77 0665 Notice that the distance 200 nautical miles must be converted to degrees of arc length with then m2 deg conversion function to match the latitude and longitude inputs If the airplane had a flight computer that allowed it to follow an exact great circle path what would the aircraft s new location be gclat gclong reckon gc 40 75 73 9 nm2deg 200 315 gclat 43 0615 gclong 77 1238 Notice also that for short distances at these latitudes the result hardly differs between great circle and rhumb line The two destinat
32. it is easy to tell which ones are right 5 17 5 Mapping Applications Bearing lines and arcs can be combined If instead of reporting a third range your radar watch had reported a bearing from the radar tower of 20 the ambiguity could have also been resolved Note however that in practice lines of bearing for navigational fixing should only be taken visually except in desperation A radar s beamwidth can be a degree or more leading to uncertainty Point A Cape Jones A i E E 1 fix iilligan s Fae Lighthouse As you begin to wonder whether this manual plotting process could be automated your first officer shows up on the bridge with a laptop and the Mapping Toolbox 5 18 Navigation Using navfix Thenavfi x command can be used to determine the points of intersection between any number of lines and arcs Be warned however that due to the combinatorial nature of this process the computation time grows rapidly with the number of objects To illustrate this function assign positions to the landmarks Point A Cape ones is at at A onA Point B the radio tower is at latB lonB Point C Gilligan s Lighthouse is at at C onC For the bearing lines only example the syntax is latfix lonfix navfix latA latB latC lonA lonB lonC 300 270 0 This defines the three points and their bearings as taken from the ship The outputs would look something
33. the Mapping Toolbox will redraw the map with the new settings undoing any cuts or trims if necessary See Chapter 4 Map Projections for information on how to project data without displaying it The toolbox also makes it easy to modify and manipulate maps The map display and mapped objects can be modified either from the command line or through graphical user interfaces and property editing tools that can be invoked by clicking on the display Most mapping display commands have graphical interfaces See Chapter 6 GUI Tools for more on these capabilities NOTE An important restriction accompanies this ease of use The Mapping Toolbox manages the map display with the User Data property field in the Axes control TheUser Data property of mapped objects is also used by the toolbox This may cause conflicts with other functions that use the User Data property field Map Axes Map Axes Todisplay maps of any kind in the Mapping Toolbox the user must first define a map axes A map axes is a normal axes that has been prepared for mapping using the a xes m command that defines the map projection properties Before you execute any mapping command you need to define a map axes in the current MATLAB axes and choose a map projection using axes m NOTE To successfully employ any map display function such asp ot m film or surf acem the current axes must be a map axes as created by axes m An axes is considered a valid ma
34. the Mapping Toolbox calculates the x y locations of the four vertices of each graticule cell and warps the matrix data to fit the resulting quadilateral 2 31 2 Displaying Maps In the toolbox as in traditional cartography the finer the graticule mesh i e the more meridians and parallels used the greater the precision of the projected map display at the cost of greater effort and time Graticules for regular matrix maps are defined in the toolbox as a two element vector of the form number of parallels number of meridians For general matrix maps the graticule is related to the size of the latitude and longitude coordinate matrices wherenumber of parallels mrows 1 and number of meri di ans ncols 1 While the graticule cell for a regular matrix map is restricted to equal angle quadrangles i e length of cell in latitude must equal length of cell in longitude general matrix maps have no such constraint Their graticule cells can be of any size Thet 0po regular matrix map can be displayed quickly using a coarse graticule The cost is in precision load topo figure axesm robinson graticule 10 20 h meshm topo topolegend graticule demcmap topo 2 32 Displaying M atrix Maps Notice that for this coarse graticule the edges of the map do not appear as smooth curves What may not be as obvious is that the easternmost column of graticule cells and the southwesternmost cell are sometimes invisible
35. the radius of the Earth is used Measuring Azimuth Azimuth is the anglea line makes with a meridian taken clockwisefrom north When the azimuth is calculated from one point to another using the Mapping Toolbox the result will depend upon whether a great circle or a rhumb line azimuth is desired For great circles the result will be the azimuth at the starting point of the connecting great circle path In general the azimuth along a great circle is not constant For rhumb lines the resulting azimuth is constant along the entire path Azimuths or bearings are returned in the same angular units as the input latitudes and longitudes The default path type is the shorter great circle and the default angular units are degrees n our example the great circle azimuth from the first point to the second is azgc azimuth 15 0 60 150 azgc 19 0391 For the rhumb line the constant azimuth is azrh azimuth rh 15 0 60 150 azrh 58 8595 1 11 I apping Fundamentals 1 12 One feature of rhumb lines is that the inverse azimuth from the second point tothefirst is the complement of the forward azimuth and can be calculated by simply adding 180 to the forward value inverserh azimuth rh 60 150 15 0 inverserh 238 8595 difference inverserh azrh difference 180 This is not true in general of great circles inversegc azimuth gc 60 150 15 0 inversegc 320 9353 difference inversegc azgc
36. 1344 26 8096 plotm points r 2 47 2 Displaying Maps 2 48 Your points will probably be different You can also use special interactive commands to interactively place text small circles and tracks For more information on these capabilities consult thegt extm scircleg andtrackg entries in the Mapping Toolbox Reference Guide along with Chapter 6 of this manual GUI Tools The Mapping Toolbox also allows you to manipulate displayed objects by name Many mapping commands assign descriptive names to theTag property of the objects they create The name functions allow you to control the display of groups of similarly named objects determine the names and change them if so desired and use the name in the Handle Graphics set and get commands Thereis alsoa Mapping Toolbox graphical user interface mobj ects tohelp you manage the display and control of objects Some mapping display functions likef ramem gridm andcont or m assign object tags by default You can also set the name upon display by assigning a string totheTag property in mapping display functions that allow property value pairs If the Tag does not contain a string the name falls back to an object s Type property such as line or text Display a vector map of the world figure axesm fournier framem on gridm on plabel on mlabel MLabel Parallel 0 load coast plotm lat long k Tag Coastline Interacting with Displayed M aps Y
37. 3 S 108 65 E lies in the Indian Ocean southwest of Australia Great Circles and Rhumb Lines In plane geometry lines have two important characteristics A line represents the shortest path between two points and the slope of such a line is constant When describing lines on the surface of a spheroid however only one of these characteristics may be guaranteed at a time In geography a great circleis the shortest path between two points along the surface of a sphere The precise definition of a great circle is the intersection of the surface with a plane passing through the center of the planet In general great circles do not havea constant azimuth thespherical analog of slope they cross successive meridians at different angles When the Earth is taken as a sphere the Equator and all meridians are great circles Great circles always bisect the sphere A rhumb lineis a complex curve the special property of which is that it crosses each meridian at the same angle This curveis also referred to as a loxodrome In general a rhumb line is not the shortest path between two points on the rhumb line All parallels including the Equator are rhumb lines since they cross all meridians at 90 Additionally all meridians are rhumb lines Rhumb lines always terminate at the poles unless the azimuth is true east or west in which case the rhumb line closes on itself to form a parallel of latitude 1 9 I apping Fundamentals A descript
38. Glossary Notes 0 cc cece cette A 2 Glossary o c cc5 see weien de cet ee hes HU eee EEEE A 3 Bibliography xi Contents Preface Preface Acknow ledgments Systems Planning and Analysis Inc SPA is proud to have developed the Mapping Toolbox The Mapping Toolbox is the product of the contributions of numerous SPA employees Ed Byrns and Eric Brown who are no longer at SPA conceived the Toolbox designed the architecture and have supported the development to its completion Walter Stumpf managed the completion of the product and also developed the external interface and the atlas data Tomi Debole and Andy Kim were essential to the development testing and documentation of the M apping Toolbox Tom Seaman wrote many of thetesting functions J uliet Crumrine edited the documentation Wendell Nix helped with the rhumb line calculations and the geometry of track intersections The product was developed with long term support from The MathWorks and many of its key employees most notably J im Tung Scott Gray J ennifer French Loren Shure and Clay Thompson In memory of J ohn Snyder whose prior work on Map Projections inspired and made possible the creation of the Mapping Toolbox Mapping Fundamentals WhatIsaMap 0 c ccc ee 1 2 Types of Maps in the Mapping Toolbox 1 3 Vector Maps sinter ew bbs eda NEN eee Sea ne ale aes 1 3 Matrix Maps i5 3 044 0 40rbe del
39. In this case thereturned mean point is NaN NaN anda warningis displayed This phenomenon is highly improbable in real data but can be easily constructed For example it occurs when all the points are equally spaced along a great circle Try taking the geographic mean of 0 0 0 120 and 0 240 which trisect the E quator G eostatistics Geographic Standard Deviation As you might now expect the Cartesian definition of standard deviation provided in the standard MATLAB function st d is also inappropriate for most geographic data Depending upon your purpose you may want to use the separate geographic deviations for latitude and longitude provided by the function st dm or the single standard distance provided inst dist Both methods measure the deviation of points from the mean position calculated by meanm The Meaning of stdm Thest dm function handles the latitude and longitude deviations separately latstd lonstd stdm lat lon The function returns two deviations one for latitudes and one for longitudes Latitude deviation is a straightforward standard deviation calculation from the mean latitude mean parallel returned by meanm This is a reasonable measure for most cases since a degree of latitude always has the same arc length Longitude deviation is another matter Simple calculations based on sum of squares angular deviation from the mean longitude mean meridian are misleading The arclength
40. Maps Hereis the result Surface Light Shading A monochrome three dimensional shaded relief map can be displayed with the function surf m which is analogous to the MATLAB surf command This functionality is available only for general matrix maps Remember that regular matrix maps are a subset of general matrix maps and can be easily converted 2 37 2 Displaying Maps Todisplay a map in this format enter the following cl ma Surflm lat lon map colormap bone This is the same region as the previous map viewed in three dimensions Notice the dramatic dip in the lower right portion of the map caused by the deep ocean trenches of the North Pacific Ocean The view is from the south at an elevation angle of 75 The light source in this case is the default 45 counterclockwise from the view direction This kind of representation shows much more of the fine structure of the land and sea floor but because of the lack of color it is difficult to distinguish land from sea 2 38 Displaying M atrix Maps Surface Lighted Shaded Relief The commands mesh srmandsurf srm display maps in alighted shaded relief format and can be thought of as extensions to sur f m that combine surface coloring and surface light shading Again mesh sr mis used for regular matrix maps ands ur f I sr m for general matrix maps Although there are no analogous MATLAB functions you can obtain similar results using MATLAB light objects
41. Massachusetts which now consist of just a handful of points The function also determined an initial default tolerance valuet ol since one was not specified as well as an error estimate of polygon arc lengths cer r between the two sets of data The tolerance value which is defined as the maximum allowable deviation from a straight line approximation is 0 006 degrees in the same angular units as the vector data and the calculated error in arc length is 3 3 tol tol 0 0060 cerr cerr 0 0331 The original vector data can be reduced even further by increasing the tolerance level Iftol is increased to 0 02 degrees the reduction is now almost tenfold with an error of about 7 7 newl at newlong cerr reducemlat long 0 02 whos Name Size Bytes Class cerr 1x1 8 double array lat 958x1 7664 double array long 958x1 7664 double array newl at 109x1 872 double array newl ong 109x1 872 double array t ol 1x1 8 double array size newlat size lat ans 0 1138 cerr cerr 0 0768 1 40 Hereis the displayed map W orking with Vector M aps reduced 109 points There is now a noticeable degradation of the line vector map along the eastern coast of the state Nonetheless it still retains much detail especially considering the enormous reduction of data NOTE Reduced geographic data may not always be appropriate for display If all intermediate points in a dataset are reduced then lines appearin
42. The following commands extract the patch data for Canada and plot it with the political line data figure axesm MapProjection eqaconic MapParallels MapLatLimit 40 90 MapLonLimit 150 45 MLabel Location 15 MLineLocation 15 PLabelLocation 15 PLineLocation 15 GColor 5 1 1 1 GLinestyle MLabel Parallel south framem gridm mlabel plabel displ aym POI ine clat clon extractm POpatch canada patchesmclat clon g Extracting and displaying only the desired data can reduce the time and memory required to display a map The Mapping Toolbox automatically trims and saves data outside the current map latitude and longitude limits If you use displ aym to show a small part of the world the rest of the world data is retained within the map axes structure E very time the projection parameters are changed all of the world data is restored trimmed and projected This overhead can be significant for a dataset as largeas worl dlo 3 11 3 Atlas Data 3 12 Apply the extraction technique to generate a display of Cape Cod As was shown in the earlier examples this data contains somewhat generalized shapes for the countries and rivers Thelevel of detail is great enough for global and regional maps but the distinct data points become noticeable when displayed for smaller regions figure axesm MapProjection mercator MapLatLimit 41 44 MapLonLimit 72
43. VI kavrsky6 Pseudocylindrical Loximuthal loxi muth Pseudocylindrical 2 McBryde Thomas Flat Polar Parabolic flatplrp Pseudocylindrical McBryde Thomas Flat Polar Quartic flatpl rq Pseudocylindrical e McBryde Thomas Flat Polar Sinusoidal flatplrs Pseudocylindrical e Mollweide mol wei d Pseudocylindrical Putnins P5 putnins5 Pseudocylindrical Quartic Authalic quartic Pseudocylindrical Robinson robinson Pseudocylindrical Sinusoidal sinusoid Pseudocylindrical Tissot Modified Sinusoidal modsine Pseudocylindrical Wagner IV wagner 4 Pseudocylindrical e Winkel winkel Pseudocylindrical Albers E qual Area Conic eqaconic Conic e Equidistant Conic eqdconic Conic Lambert Conformal Conic lambert Conic Murdoch Conic mur doch Conic e 3 Murdoch III Minimum Error Conic murdoch3 Conic 3 Summary Guide un g B E 2 T g 1 D 7 r I 5 5 o Projection Syntax Type g 8 g Fi Bonne bonne Pseudoconic Werner werner Pseudoconic Polyconic polycon Polyconic Van Der Grinten vgrintl Polyconic Breusing Harmonic Mean breusing Azimuthal E quidistant Azimuthal eqdazim Azimuthal Gnomonic gnomonic Azimuthal 4 Lambert Azimuthal Equal Area egaazim Azimuthal Orthographic ortho Azimuthal Stereographic stereo Azimuthal e 5 Wiechel wi echel Pseudoazimuthal Globe globe Spherical e 6 1 Straight rhumb lines 2 Rhumb lines from central point are straight true to scale a
44. W c 270 lt fix at 0800 course change 10 2 at 0900 5 31 5 Mapping Applications However Mr Bowditch shoots the sun at local apparent noon and discovers that the ship s latitude is actually 30 29 N What s worse he lives before the invention of a reliable chronometer and so he cannot calculate his longitude at all from this sighting What happened Leaving aside the difficulties in speed determination and the need to tack off course even modern craft have to contend with winds and currents However despite these limitations dead reckoning is still used for determining position between fixes and for forecasting future positions This is because dead reckoning provides a certainty of assumptions that estimations of wind and current drift cannot When navigators establishes a fix from some source be it from piloting celestial or satellite observations they plot a dead reckoning DR track which is a plot of the intended positions of the ship forward in time In practice dead reckoning is usually plotted for 3 hours in advance or for the time period covered by the next three expected fixes In open ocean conditions hourly fixes are sufficient in coastal pilotage three minute fixes are common Specific DR positions which are sometimes called DRs are plotted according to the Rules of DR e DR at every course change e DR at every speed change e DR every hour on the hour e DR every time
45. a logical map can be created by testing conditions on several layers of maps logical map population gt 10000 amp elevation lt 400 amp country ni geri a The Mapping Toolbox provides functions that enable the creation of logical maps F or example the 5 cell per degree maps covering the continental United States of all 1s and all Os can be easily constructed latlims 25 55 longlims 130 60 scale 5 onesmap onem latlims longlims scale zeroesmap zeromlatlims onglims scale Maps of all Na Ns and sparse maps of all Os can be madein a similar fashion with the commands nanm ands pzerom A useful way of analyzing the results of logical map manipulations is to determine the area satisfying the conditions i e with a logical value of 1 The command areamat can provide the fractional surface area on the globe associated with 1s in a logical map Each matrix element is a quadrangle and the sum of the areas meeting the logical condition provides the total area F or example according to thet opo map what fraction of the Earth lies above sea level load topo a areamat topo gt 0 topol egend a 0 2890 1 51 I apping Fundamentals The answer is about 30 If a planetary radius is provided in for example kilometers the total physical area above 0 elevation can be returned in square kilometers a a areamat topo gt 0 topolegend al manac earth radius 1 4739e 08 Tointerp
46. calculating 5 28 connecting 5 29 defined 5 13 selecting with mouse 5 29 6 26 world matrix data finding countries from coordinates 3 15 political data 3 14 terrain data 3 17 world vector data atlas data 3 5 coastline data 3 3 deleting data with tags 3 9 displaying atlas data 3 5 extracting data with tags 3 11 wor di o workspace 3 5 activating from mapt oo 6 7 worl dmt x workspace 3 14 Z zero22pi 1 8 zerom 1 51 Index zoom GUI 6 11 1 11
47. center of the circle while the other limit determines the radius of the circular frame rlatmax The longitude limits of azimuthal frames are inconsequential since a full circleis always displayed If you are uncertain about the correct format for a particular projection frame limit you can reset them to the default values using empty matrices NOTE For non azimuthal projections in the normal aspect the map is limited to the minimum of the map and frame limits hence the two limits will coincide after evaluation When changing one set of limits you may want to clear the other set to get consistent limits Switching Between Projections Switching Between Projections When switching between projections using s et m or the graphical interfaces you may need to change some of the map axes properties for proper appearance Settings that are suitable for one projection may not be appropriate for another Some projections have default properties that define that particular projection and may not be altered for example the Balthasart Cylindrical projection is defined to have standard parallels MapParallels at 50 Other projections have default properties that are initially set for proper world display for example the Mercator projection limits the latitude range to 86 to avoid blowing up at the poles Although similar projections may share the same set of properties Miller Cylindrical and Plate Carree Cylindrical o
48. command window Enter the following citylats 39 17 51 59 41 53 45 27 53 55 citylons 76 86 0 04 2 25 12 21 9 70 6 12 The Complete GUI Environment maptool Press Apply when you have finished Workspace Commands Statements to execute citylats 39 17 51 59 41 53 45 27 53 55 citylons 76 86 0 04 2 25 1 71 9 701 A Status Report box appears to indicate that the operations were successful Press OK Select Session gt Variables fromthe menu bar and you will seethe two new variables in the workspace Press Close to close the Current Variables box Plotting Line Objects To plot the cities choose Map gt Lines from the menu bar The Line Map Input Box appears Enter the latitude and longitude variables ci t yl ats and citylons Inthe Other Properties edit box type r toplot a red marker at each city location Press Apply Line Map Input gt Latitude variable citylats Longitude variable citylons Altitude variable optional 1 Other Properties tema e kexsat 6 13 6 14 6 G UI Tools The city markers now appear on the map Figure No 1 als Plotting Text Objects Toplot city names select Map Text from the menu bar The Text Map Input dialog box appears In the Text variable string edit box type strvcat Washington DC London Barcelona Venice Hamburg
49. did for the previous map first select Session Command from the menu bar Enter the following in the Workspace Command dialog box lats 41 53 43 44 43 33 42 19 41 01 45 27 fons 2 25 7 25 11 12 47 14 22 12 21 Press Apply when done Workspace Commands Statements to execute 6 23 6 G UI Tools Next select Map gt Lines from the menu bar Enter the Latitude variable lats and the Longitude variable ons in the appropriate edit boxes along with thelinestyle r and Tag City Markers inthe Other Properties edit box Press Apply when done Line Map Input Latitude variable C Ce Longitude variable lons List Altitude variable optional Other Properties r Tag City Markers Finally select Map Text from the menu bar Enter the following in the Text variable string edit box strvcat Barcelona Monte Carlo Livorno Rome Naples Venice Enter the variables ats and ons in the Latitude variable and Longitude variable edit boxes respectively In the Other Properties edit box enter the following FontSize 8 Tag City Labels 6 24 The Complete GUI Environment maptool Press Apply when you have finished Text Map Input gt gt Text variable string strvcatt Barcelona Mo Latitude variable Longitude variable Scalar Altitude o
50. display the data as a line whilefi m will display it as a filled polygon When vector variables are used to represent several segments or polygons successive objects should be delineated by the insertion of NaNsin both variables For example if a second segment is to be added to the above map the two objects can reside in the same pair of variables lat 45 6 23 47 78 NaN 43 9 67 14 90 89 long 13 97 45 165 NaN 0 114 2 18 0 Notice that the Na Ns must appear in the same locations in both variables Here we havea segment of three points separated from a segment of four points The NaNs perform two functions they provide a simple means of identifying break points in the data and they act as pen up commands when plotting vector maps The NaNs are also used in the Mapping Toolbox to separate non connected patch faces NOTE This definition differs from MATLAB which does not display NaN clipped data as patches 1 25 I apping Fundamentals Segments versus Polygons Geographic objects represented by vector data may or may not be formatted as polygons I magine two variables at coast and oncoast which correspond to sequential points around the coast of the island of Great Britain If this data returns to its starting point then a polygon formatted map of Great Britain exists This data might be plotted as a patch or as a line and it might be logically employed in calculations as either Now cons
51. follow a great circle path one would have to continuously alter course This is impractical However a great circle path can be approximated by rhumb line segments so that the added distance is minor and the number of course changes minimal Surprisingly very few rhumb line track legs are required to closely approximate the distance of the great circle path Consider the voyage from Norfolk Virginia 37 N 76 W to Cape St Vincent Portugal 37 N 9 W one of the most heavily trafficked routes in the Atlantic A due east rhumb linetrack is 3 213 nautical miles in length whilethe optimal great circle distance is 3 141 nautical miles Although the rhumb line path is only a little more than 2 longer this is an additional 72 miles over the course of the trip For a 12 knot tanker this results in a 6 hour delay and in shipping time is money If just three rhumb linesegments are used to approximate the great circle the total distance of the trip is 3 147 nautical miles Our tanker would suffer only a half hour delay over optimal Zr S 3 Leg Approximation 3147 nm n n a Direct Course 3213 nm Io f 5 27 5 Mapping Applications The Mapping Toolbox provides the function gc waypts to quickly calculate waypoints in navigation track format in order to approximate a great circle with rhumb line segments The syntax is simple latpts lonpts gcwaypts lati1 lon1 at2 lon2 num egs All of
52. g e Balthasart balthsrt Cylindrical e Behrmann behr mann Cylindrical Bolshoi Sovietskii Atlas Mira bsam Cylindrical Braun Perspective braun Cylindrical Cassini cassini Cylindrical Central ccylin Cylindrical E qual Area Cylindrical eqacylin Cylindrical Equdistant Cylindrical eqdcylin Cylindrical Gall Isographic giso Cylindrical e Gall Orthographic gortho Cylindrical 4 22 Summary Guide wn g B E ee 1 D 7 3s Z 53 5 o Projection Syntax Type g g amp Gall Stereographic gstereo Cylindrical Lambert E qual Area Cylindrical lambcyln Cylindrical M ercator mercator Cylindrical 1 Miller miller Cylindrical Plate Carree pcarree Cylindrical Trystan Edwards trystan Cylindrical e Wetch wetch Cylindrical Apianus lI api anus Pseudocylindrical Collignon collig Pseudocylindrical Craster Parabolic craster Pseudocylindrical Eckert eckertl Pseudocylindrical Eckert II eckert2 Pseudocylindrical Eckert III eckert3 Pseudocylindrical Eckert IV eckert4 Pseudocylindrical Eckert V eckert5 Pseudocylindrical Eckert VI eckert 6 Pseudocylindrical Fournier fournier Pseudocylindrical Goode Homolosine goode Pseudocylindrical H atano Assymetrical Equal Area hat ano Pseudocylindrical e 4 23 4 M ap Projections 4 24 v g g e S ge g T amp n amp so I 53 5 o Projection Syntax Type g g amp Kavraisky V kavrsky5 Pseudocylindrical Kavraisky
53. help mode for that particular GUI Once in help mode pressing any enabled control will display the help text for that control in a separate help box Pressing the Done button will close the help box and end help mode This chapter is a short tutorial on several of the Mapping Toolbox GUI tools For a more detailed description of each tool consult the GUI Reference section of the Mapping Toolbox Reference Guide The Complete GUI Environment maptool The Complete GUI Environment ma pt oo In this section mapt ool is used to access many of the Mapping Toolbox GUIs It should be noted however that most of the Mapping Toolbox GUIs can be activated independently at any time during a mapping session without the use of maptool The GUI Reference section of the Mapping Toolbox Reference Guide provides details on the methods for activating each tool Starting maptool You can start maptool in one of three ways maptool maptool MapProjectionName maptool MapPropertyName MapPropertyValue Starting mapt ool creates a new figure window with a map axes and a set of pull down menus File Edit Window Session Map Oispl ay Tools Colormaps Figure No 1 6 3 6 G UI Tools All mapping functions activated through mapt oo will be associated with this map axes If an initial map projection is not provided at the command line the Projection Control dialog box will appea
54. is equally distant from but on the opposite side of the Equator For example for lat 30 N or 30 the parallel of opposite sign is lat 30 S or 30 Also called latitude of opposite sign Parameters The values of constants as applied to a map projection for a specific map examples are the values of the scale the latitudes of the standard parallels and the central meridian The required parameters vary with the projection Perspective projection A projection produced by projecting straight lines radiating from a selected point or from infinity through points on the surface of a sphere or ellipsoid and then onto a tangent or secant plane Other perspective maps are projected onto a tangent or secant cylinder or cone by using straight lines passing through a single axis of the sphere or ellipsoid Also called geometric projection Planar projection A projection resulting from the conceptual projection of the Earth onto a tangent or secant plane Usually a planar projection is the same as an azimuthal projection Mathematically the projection is often only partially geometric Planimetric map A map representing only the horizontal positions of features without their elevations Polar aspect An aspect of a projection especially an azimuthal one on which the Earth is viewed from the polar axis For cylindrical or pseudocylindrical projections this aspect is called transverse Pole An extremity of a planet s axis
55. like this with actual numbers of course latfix atfixl a A intersecting B atfix2 Na A intersecting C atfix3 a B intersecting C lonfix onfi xl a A intersecting B onfi x2 Na A intersecting C onfi x3 a B intersecting C Notice that these are two column matrices The second column consists of NaNs because it is used only for the two intersection ambiguity associated with arcs For the range arcs only example the syntax is latfix lonfix navfix latA latB latC lonA lonB lonC 16 14 15 0 0 0 This defines the three points and their ranges as taken from theship The final argument indicates that the three cases are all ranges 5 19 5 Mapping Applications The outputs have the following form latfix atfixll atfixl2 A intersecting B atfix21 atfix22 A intersecting C atfix3l atfix32 B intersecting C lonfix onfixll onfixl2 A intersecting B onfix21 onfix22 A intersecting C onfi x31 onfix32 B intersecting C Here the second column is used because each pair of arcs has two potential intersections For the bearings and ranges example the syntax requires the final input to indicate which objects are lines of bearing indicated with a 1 and which are range arcs indicated with a 0 latfix lonfix navfix latB latB latC lonB lonB lonC 20 14 15 1 0 0 The resulting output is mixed latfix atfixll NaN Line B inter
56. normal and transverse aspects can be thought of as limiting conditions Anything else is an oblique aspect Conceptually if you push the North Pole halfway back to its original position that is to the position originally occupied by the point 45 N 0 in the normal aspect the result will be a simple oblique aspect 4 11 4 M ap Projections 4 12 Here is the oblique aspect Sinusoidal projection Oblique Aspect Origin at 45 N 0 Orientation 0 origin vector 45 0 0 Another way of understanding this is to imagine the new origin point 45 N 0 being pulled to the center of the image to the point originally occupied by 0 0 in the normal aspect The examples so far have left the aspect orientation at 0 If the orientation is altered an oblique aspect becomes a skew oblique Imagine the previous example with an orientation of 45 Conceptually the skew oblique aspect corresponds to pulling the new origin point 45 N 0 down to the center of the projection and then rotating the projection until the North Polelies at an angle of 45 clockwise from straight up with respect to the new origin Projection Aspect Here is the result Skew Oblique Aspect Origin at 45 N 0 Orientation 45 origin vector 45 0 45 Any projection can be viewed in alternate aspects Some of these are quite useful For example the transverse aspect of the Mercator projection is widely used in cartogra
57. normal aspect with respect to this transformed coordinate system the resulting display would look like an oblique aspect with respect to the true coordinate system This transformation of coordinate systems can be useful independent of map displays If a transformed coordinate system is selected so that your hometown is the new north pole then the transformed coordinates of all other points will provide interesting information The distance of each point from your hometown is then simply 90 minus the transformed latitude F or example the point antipodal to your hometown would be the transformed south pole 90 Its distance from your hometown is then 90 90 or 180 as expected Points 90 distant from your hometown all have a transformed latitude of 0 In fact these points make up the transformed equator The transformed longitudes correspond to the great circle azimuths of those points from your hometown When regular matrix maps are transformed in this manner distance and azimuth calculations with the map variable reduce to row and column operations 4 14 Projection Aspect Vector Data rotatem As an example of transforming a coordinate system suppose you live in Midland Texas at 32 N 102 W You have a brother in Tulsa 36 2 N 96 W and a sister in New Orleans 30 N 90 W midl lat 32 midl lon 102 tuls_lat 36 2 tuls_lon 96 newo_lat 30 newo_lon 90
58. of rotation The North Poleis a singular point at 90 N for which longitude is ambiguous The South Pole has the same characteristics and is located at 90 S Polyconic projectio A specific projection or member of a class of projections that are constructed like conic projections but with different cones for each parallel In the normal aspect all the parallels of latitude are nonconcentric circular arcs except for a straight Equator and the centers of these circles lie along a central axis Projection A systematic representation of a curved 3 D surface such as the Earth onto a flat 2 D plane Each map projection has specific properties that make it useful for specific purposes A 11 A Geographic Terms Pseudoconic projection A projection that in the normal aspect has concentric circular arcs for parallels and on which the meridians are equally spaced along the parallels like those on a conic projection but on which meridians are curved Pseudocylindrical projection A projection that in the normal aspect has straight parallel lines for parallels and on which the meridians are usually equally spaced along parallels as they areon a cylindrical projection but on which the meridians are curved Quadrangle A region bounded by parallels north and south and meridians east and west Raster map See Matrix map Reckoning The determination of geographic position by calculation Regional map A small scale map of
59. on displayed matrix maps This is necessary for the proper projection of the surface object and is not a concern except with the coarsest graticules Previous displays used the default 50 100 graticule for which this effect is negligible Regardless of the graticule resolution the matrix map data is unchanged In this case the matrix map is the 180 by 360 t opo matrix and regardless of projection fidelity the resolution of its value data is unchanged Map objects displayed as surfaces have all the properties of any MATLAB surface which can be set at object creation or by using the MATLAB set command The mappings et m command allows theMeshGr at graticule property to be manipulated for regular matrix surfaces Since you saved the handle of the last displayed map reset its graticule toa very fine grid Remember the trade off is between resolution and time so this could take a while setmh MeshGrat 200 400 2 33 2 Displaying Maps You ll probably notice that the result does not appear to be any better than the original display with the default 50 100 graticule but it took much longer to produce Actually the 200 by 400 graticule grid is finer than the 180 by 360 data resolution There is really noreason to ever use a graticulefiner than your data In practice you will probably find that coarse graticules are good for development tasks and fine graticules serve well for final graphics production Coloring Matrix Maps
60. represented by a degree of longitude at extreme latitudes is significantly smaller than that at low latitudes Theterm departureis used to represent the arc length distancealonga parallel of a point froma given meridian For example assuming a spherical planet the departure of a degree of longitude at the E quator is a degree of arc length but the departure of a degree of longitude at a latitude of 60 is one half a degree of arc length Thes t dm function calculates a sum of squares departure deviation from the mean meridian 5 5 5 Mapping Applications If you want to plot the one sigma lines for s t dm the latitude sigma lines are parallels However the longitude sigma lines are not meridians they are lines of constant departure from the mean parallel ee ee eee or ee ee a ee eo ee ee ee ee ee ee eC ee a eee ee ee ae a ee er eee ae me ee er me Latitude one sigma lines are parallels Mean Position Longitude one sigma lines are not meridians This handling of deviation has its problems F or example its dependence upon the logic of the coordinate system can causeit to break down near the poles F or this reason the standard distance provided byst di st is often a better measure of deviation Thes t dm handling is useful for many applications especially when the data is not global For instance these potential difficulties would not be a danger for data points confined to the country of Mexico The Meaning of stdist T
61. scale at specific points Other terms for equal area projections include equivalent homolographic or homalographic from the Greek homalos or homos same and graphos write authalic from the Greek autos same and ailos area and equireal A conformal projection is one that preserves the relative local angles shape about every point on the map except for one or more possible singular points Since relative local angles are correct meridians intersect parallels at right angles 90 degrees No map can be both equal area and conformal Another term for conformal is orthomorphic from the Greek orthos straight and morphe shape An equidistant projection shows true scale between oneor two points and every other point on the map or along every meridian No map projection shows scale correctly in all directions throughout the entire map 4 3 4 M ap Projections Geometric Surfaces Three standard types of geometric surfaces are used to develop map projections the cylinder the cone and the plane A few projections however cannot be categorized as such or are combinations of these The three classifications are used for a wide variety of projections including some that are not geometrically constructed A cylindrical projection is produced by wrapping a cylinder around a globe representing the Earth The map projection is the image of the globe projected onto the cylindrical s
62. specific latitude at which the meridian labels will be displayed and theP Label Meri di an allows the choice of west east prime or aspecificlongitude for the parallel labels Refer to thea x esm reference pagein the Mapping Tool box Reference Guidefor complete descriptions of all map axes properties 2 17 2 Displaying Maps 2 18 Map and Frame Limits In the Mapping Toolbox the map and frame limits are two related map axes properties that limit the map display to a defined region The map latitude and longitude limits restrict the displayed parallels and meridians while the frame limits control the extent of the frame around the displayed data Any object that extends outside the frame limits is automatically trimmed The frame limits are also specified differently from the map limits The map limits are in Greenwich coordinates referenced to an origin at the intersection of the Prime Meridian and the Equator while the frame limits are in coordinates referenced to the center of the frame which is the latitude and longitude of the map axes origin For all non azimuthal projections frame limits are specified as quadrangles Il atmin atmax and ongmin ongmax in the frame coordinate system In the case of azimuthal projections the frames are circular and are described by a polar coordinate system One of the frame latitude limits must be a negative infinity I nf to indicate an azimuthal frame think of this as the
63. the 3 The point 1 5 2 was therefore interpolated and placed into newl ats andnewl ongs Now noadjacent points in either newl ats or newl ongs is greater than maxdi ff in separation Thei nt er pm function returns the original data with new linearly interpolated points inserted Sometimes however only the interpolated values are desired The commandsi ntrplat andi ntrpl on provide a capability similar to MATLAB Si nt erp1 command allowing for different methods of interpolation Usei ntrpl at tointerpolatea latitude for a given longitude Given a monotonic set of longitudes and their matching latitude points you can interpolate a new latitude for a given longitudein a linear spline cubic rhumb line or great circle sense 1 31 10 apping Fundamentals Here find the latitude corresponding toa longitude of 7 3 in the following data in a linear great circle and rhumb line sense longs 1 3 4 9 13 lats 57 68 60 65 56 newlong 7 3 newlat intrplat longs lats newlong linear newlat 63 3000 newlat intrplat longs lats newlong gc newlat 63 5029 newlat intrplat longs lats newlong rh newlat 63 3937 65 9 great circle latitude 63 3937 rhumb line latitude 63 502 9 linear latitude 63 3000 60 4 longitude 7 3 Thei ntrpl on function provides the same capability for interpolating new longitudes for given latitudes Polygon Area For vector data in polygon fo
64. the Zoom button in the upper left corner of the figure Zoom mode can also be activated by selecting Tools gt Zoom Tool from the menu bar or with the command panzoom A red zoom box will appear on the map once the zoom feature has been activated Drag the box until it encompasses the eastern half of the United States and most of Europe as shown below You can resize the box by clicking near a corner within the box and dragging the corner Double click inside the box to zoom in rm Zm Figure No 1 zeom 6 11 6 G UI Tools Here is the zoomed in region Click the Zoom button to end Zoom mode or press Esc if you used the panzoom command zm Figure No 1 a3 You can zoom out again by selecting Tools gt Full View from the menu bar For more information on the Zoom feature see the GUI Reference section of the Mapping T oolbox Reference Guide Entering Workspace Commands Now plot the cities that are on your flight schedule Washington D C London Barcelona Venice and Hamburg You will need two variables containing the latitude and longitude coordinates of these cities Select Session Command from the menu bar The Workspace Commands dialog box appears This dialog box allows command line statements to be executed directly from mapt oo rather than from the MATLAB
65. the inputs for this command are scalars Thenuml egs input is the number of equal length legs desired which is 10 by default The outputs are column vectors representing waypoints in navigational track format The size of each of these vectors will be numlegs 1 1 Here are the points for the example illustrated above latpts lonpts gcwaypts 37 76 37 9 3 latpts 37 0000 41 5076 41 5076 37 0000 lonpts 76 0000 54 1777 30 8223 9 0000 These points represent waypoints along the great circle between which the approximating path follows rhumb lines F our points are needed for three legs because the final point at Cape St Vincent must be included Track Laydown Displaying Navigational Tracks Navigational tracks are most useful when graphically displayed Traditionally the navigator identifies and plots waypoints on a M ercator projection and then connects them with a straightedge which on this projection results in rhumb line tracks In the previous example waypoints were chosen to approximate a great circle route but they may be selected for a variety of other reasons Let s say that after arriving at Cape St Vincent your tanker must traverse the Straits of Gibraltar and then travel on to Port Said the northern terminus of the Suez Canal On the scale of the Mediterranean Sea following great circle paths is of little concern compared to ensuring that the many straits and passages are safely transited The nav
66. their display and by their altitude position For this reason the primary patch display function in the Mapping Toolbox f i m allows you to control the z axis level of displayed patches Here the land data is displayed at the default level z 0 The Great Lakes data is assigned the altitude of z 1 To plot the line segment data between these layers use the pI ot 3m command and specify an altitude of 0 5 fillm uslat uslon FaceColor 1 5 3 EdgeColor none fillm gtlakelat gtlakelon 1 FaceColor cyan EdgeColor none plot3mstatelat statelon 0 5 k 2 28 Displaying Vector Maps as Patches Hereis the result Thef i 1m function makes use of the low level function pat chm The Mapping Toolbox provides another patch drawing function called pat ches m The optimal use of either depends on the application and user preferences The pat chm function creates one displayed object and returns one handle for a patch which may contain multiple not necessarily connecting faces The Mapping Toolbox uses NaNs to Separate non connected patch faces unlike MATLAB which does not handle NaN clipped data for patches For thepat ches m function each face is a separate object with its own handle In general pat chm requires more memory but is faster than pat chesm 2 29 2 Displaying Maps 2 30 Displaying Matrix Maps The Mapping Toolbox provides functions for the display and enhancement of both regular an
67. to the map axes To plot the map of J apan using the Mesh Map Input dialog box type mes hm Mesh Map Input Map variable Maplegend variable Graticule size variable L50 100 List Altitude variable optional C g Other Properties Your variable names are the same as the defaults so press Apply to plot the map After the mapis plotted typecol or map clr map This will set the current colormap to the customized one you created To annotate the major bodies of water in the display typet ext m Constructing Personalized Map Data with G Uls The Text Map Input dialog box appears In the Text variable string edit box enter the following strvcat Sea of Japan Pacific Ocean In the Latitude variable edit box enter 39 31 and in the Longitude variable edit box enter 130 137 In the Other Properties edit box enter FontSize 9 and Font Weight bold Text Map Input Text variable string strvcat Sea of Japan Latitude variable Longitude variable 1130 137 Scalar Altitude optional C Lice Other Properties FontSize 9 FontWeight bold Press Apply to plot the text 6 43 6 Gu Tools The final display of your customized map of J apan appears as follows Sea of Japan Pacific Ocean External Data Interface Working With External Data 0 7 2 Global
68. 0 double array g2 50x50 20000 double array ltl 50x50 20000 double array lt 2 50x50 20000 double array map1 50x50 20000 double array ma p 2 50x50 20000 double array Two general matrix maps are in this workspace each requiring three variables The values contained in map1 correspond to the latitude and longitude coordinates respectively in t 1 and g1 Notice that all three matrices are the same size Similarly map2 1t2 andl g2 together forma second general matrix map These datasets were extracted from thet opo matrix map shown in previous examples Neither of these maps is regular in that their columns do not run north and south 1 53 I apping Fundamentals To get an idea of their geography display them together Notice that neither map is a regular rectangle One looks like a diamond geographically the other like a trapezoid The trapezoid is displayed in two pieces because it crosses the edge of the map These shapes can be thought of as the geographic organization of the data just as rectangles are for regular matrix maps But just as for regular matrix maps this organizational logic does not mean that displays of these maps are necessarily a specific shape W orking with M atrix Maps Here you can view these maps together in a Polyconic projection Since the Polyconicis limited toa 150 range in longitude those portions of the maps outside this region are trimmed automatically 1 55 I apping Fundament
69. 2 28 2 29 filtering geographic data 5 11 filterm5 11 findm 1 48 fipsname 7 19 7 21 fixing Seenavigational fixing frame See map frame framem 2 11 2 14 G gcwaypts 5 12 5 28 gcxgc 1 34 gcxsc 1 34 general matrix maps defined 1 53 displaying 2 30 image and surface coloring 2 36 light shading 2 37 shaded relief 2 39 Seealso matrix maps geographic data structure defined 2 43 displaying 2 45 extracting data from 3 11 3 21 geographic mean 5 3 geographic standard deviation 5 5 geoid availability for planets 1 19 converting ellipsoid parameters 1 17 defined 1 16 Index ellipsoid approximation 1 16 ellipsoid models for Earth 1 18 geoid vector 1 17 geostatistics calculating geographic mean 5 3 calculating geographic standard deviation 5 5 equal area coordinate system 5 10 equirectangular binning 5 8 filtering data sets 5 11 histograms 5 8 getm 2 6 gnomonic projection 4 6 graphical user interfaces activating 6 2 getting help 6 2 See also ma pt oo graticule choosing resolution 2 32 2 33 defined 1 56 2 31 great circles approximating tracks with rhumb lines 5 28 calculating points of 1 28 defined 1 9 grid S map grid grn2eqa 5 10 H handl em 2 49 hi dem 2 49 histograms 5 8 histr 5 8 hms notation 1 23 hours notation 1 23 l indexed maps defined 1 50 modifying colormap 6 41 replacing values 6 33 i nput m 2 47 5 29 6 26 interplat 1 31 interplon 1 31 interpm 1 30 interpolation latitude
70. 45 12 W orking with Vector M aps For the great circle from 31 S 90 E to 23 S 110 E uset rack2 latgc longc track2 gc 31 90 23 110 track1 track2 output points final point yx 1 7 7 Te i 7 7 initial point oe initial point Z o p e output points azimuth and range Thetrack1 function also allows range endpoints to be specified For example if you want points along a rhumb line starting 5 away from the initial point and ending 13 away at an azimuth of 55 simply specify the range limits latrh lonrh track1 rh 31 90 55 5 13 track1 with range limits output points g 7 4 2 Ca 7 oo P azimuth initial point m range2 When no range is provided for t rack1 the returned points represent a complete track For great circles a complete track is 360 encircling the planet and returning to the initial point For rhumb lines the complete track terminates at the poles unless the azimuth is 90 or 270 in which case the complete track is a parallel that returns to the initial point 1 29 I apping Fundamentals For calculated tracks 100 points are returned unless otherwise specified Y ou can calculate several tracks at one time by providing vector inputs See the reference pages ont rack1 andtrack2 inthe Mapping Toolbox ReferenceGuide for more information More vector path calculations are described later in Chapter 5 of this document under the sectio
71. 6 56 0501 56 0355 55 9937 56 0168 55 8413 5 23 5 Mapping Applications Here s what these points look like Point A 5 24 Navigation Three of these points look reasonable three do not What if instead of a range from Point A you had a bearing to it of 284 newlat newlong navfix lata latb latc lona lonb lonc 284 9 7 5 1 0 0 newlat 3 0526 2 9892 3 0592 3 0295 3 0443 3 0880 newlong 56 0096 55 7550 56 0360 55 9168 56 0168 55 8413 Point B ON a ee N 5 25 5 Mapping Applications Again visual inspection of the results indicates which three of the six possible points seem like reasonable positions When using the dead reckoning position 3 05 N 56 0 W the closer more reasonable candidate from each pair of intersecting objects is chosen drlat 3 05 drlon 56 newlat newlong navfix lata latb latc lona lonb lonc 284 9 7 5 1 0 0 drlat drlon newlat 3 0526 3 0592 3 0443 newlong 56 0096 56 0360 56 0168 Point C KS Dead Reckoning tp Position The selected points 5 26 Navigation Planning We know that the shortest path between two geographic points is a great circle Sailors and aviators areinterested in minimizing distancetravelled and hence delay We also know that the rhumb lineis a path of constant heading the natural means of travelling In general to
72. 69 framem gridm MLineLocation 1 PLineLocation 1 ml abel MLabel Location 1 plabel PLabelLocation 1 lat lon extractm POpatch united states patchesm lat lon FaceColor 5 1 1 1 447 WwW 7i W 70 W 69 W 43 42 41 W orld Vector Data Thewor l dl o atlas data can also be used to look up names and locations All of the names mentioned in thePOtext andPPtext structures are collected in a gazette structure which can be queried using extract m For example the location of the city of Antananarivo on the island of Madagascar can be found by using the following commands lat long indx extractm gazette antan gazette indx ans type line otherproperty tag Antananarivo string Populated Place Name altitude lat 18 6900 long 47 4480 A much more extensive gazette feature can be found in the Digital Chart of the World DCW containing more than 10 000 names compared to about 500 in theworl dl o MAT file See Chapter 7 External Data Interface for more information on the DCW 3 13 3 Atlas Data World Matrix Data Political The Mapping Toolbox includes a set of matrix data coded with political information in the MAT filewor dmt x load worl dmt x whos Name Size Bytes Class cl r map 195x3 4680 double array map 180x360 518400 double array mapl egend 1x3 24 double array nations 1x195 21324 Struct array The variable map is a regu
73. 71 W 70 W 69 W 44 43 42 ay 7 22 G lobal Gridded Elevation Data Global Gridded Elevation Data Digital Elevation Models DEMs represent another class of useful geographic data These are matrices of land elevations and ocean depths generally on a regular grid Thet opo workspacein MATLAB is an example of alow resolution DEM with cells that extend 1 degree by 1 degree giving a spatial resolution of about 100 kilometers or better The Mapping Toolbox provides interfaces to more detailed DEMs ranging in resolution from 10 kilometers to 100 meters ETOPOS and TerrainBase ETOPO5 and TerrainBase are digital elevation models with worldwide coverage at a resolution of 5 minutes 10 kilometers or better They are both compilations of data from a variety of different sources including the U S Naval Oceanographic Office U S Defense Mapping Agency U S Navy Fleet Numerical Oceanographic Center Bureau of Mineral Resources in Australia and the Department of Industrial and Scientific Research in New Zealand The ETOPO5 dataset was assembled by Margo E dwards at Washington University in St Louis Missouri An overview of this dataset can be found at several Internet locations including the U S Geological Survey Web site located at http edcwww cr usgs gov and the U S National Geophysical Data Center home page at http www ngdc noaa gov The ETOPO5 data is read using theet 0po5 external interface fun
74. Axes Properties Similarly the possible property values and their defaults can be displayed with thes et m command alone set m gc Angl eUni Aspect FixedOri Geoid MapLatl MapLonl MapPara MapPr oj NParal Origin Tri mlat Tri mLon Frame FEdgeCo FFaceCo Re a ts ent i mi t i mi t lels ection els lor lor FLatLi mit FLi neWi dth FLonLi mit Grid GAltitu GColor GLi nest GLi ne Wi MLi neEx MLi neFi MLi neLi MLi neLo MLineV PLi neEx PLi neFi PLi neLi PLineLo PLi neVi Font Ang de yle dth ception mi t cation sible ception l mi t cation sible le degrees radians dms dm normal transverse FixedOrient is a read only property NParallels is a read only property TrimLat is a read only property TrimLon is a read only property on off on off poer ee a Aa on off on off normal italic oblique 2 9 2 Displaying Maps FontColor Font Name FontSize FontUnits inches centimeters points pixels Font Wei ght normal bold Label For mat compass Label Units degrees MeridianLabel on off MLabel Location MLabel Parallel MLabel Round Parallel Label on off PLabel Location PLabel Meri dian PLabel Round Properties can also be displayed individually setm gca AngleUnits AngleUnits degrees setm gca MapProjection normalized
75. Figure No 1 The Complete GUI Environment maptoo l Plotting Layered Atlas Data Select Session gt Layers gt World LoRes from the menu bar to activate the ml ayers GUI with thewor d o workspace File Edit Window ERRULE map Display Tools Colormaps toad P Layers gt World LoRes JS LoRes Renderer USA HiRes Variables Workspace Command Other This brings up the worldlo dialog box which lists all the structures in the wor dl o workspace Wworldlo DNline BNpateh POpate h POtext PP poi nt PPtext Prepesty members Purse 6 7 6 G UI Tools Select P 0 i ne in thelist box and press the Plot button Pressing the Members button reveals that the PO line data consists of two object sets Coast ine and International Boundary Object Sets in POline International Boundary Coastline Press the Close button Y our figure now displays coastlines and international boundaries O Figure No 1 E Close the worldlo dialog box Thewor dl o variables associated with the dialog box have been removed but the plotted objects remain on the map The Complete GUI Environment maptool Editing Object Properties Toview and edit properties of currently mapped objects usethemobj ects GUI Select Tools and Objects from the menu bar The Objects Sets dialog box appears which list
76. N to 70 N Long 90 W to 90 E Lat 70 S to 30 S Long 60 E to 150 E Lat 90 S to 0 Long 180 W to 30 W For the frames shown above the projection is centered on the Prime Meridian or 0 longitude Such a frame would be the result of creating a map axes with the defaults for the Robinson projection and then resetting the frame limits to cover just part of the world For example to view the asymmetric frame in the lower right of the previous figure type axesm robinson setmgca FlatLimt 70 30 FLonLimit 60 150 Frame on 2 12 The Map Frame When you want your frame to be symmetric about the region of interest have axesm determine the proper settings for you If you specify the map limits without specifying the map origin and frame limits axes m will automatically set the appropriate values for a proper symmetric frame Frame Quadrangles Shown in the Robinson Projection Symmetric about Map Limits Lat 30 N to 70 N Long 90 W to 90 E Lat 90 S to 0 Lat 70 S to 30 S Long 180 W to 30 W Long 60 E to 150 E For example to view the symmetric frame in the lower right of the previous figure set the map limits with axes m axesm MapProjection robinson MapLatLimt 70 30 MapLonLimit 60 150 Frame on 2 13 2 Displaying Maps In addition to the latitude and longitude limits of the frame other prope
77. Situations 0 020 ee eee eee 5 14 Using navfix 0 0 ee tee 5 19 A Numerical Example of Using navfix 5 21 Planning 1 ee as 5 27 Track Laydown Displaying Navigational Tracks 5 28 Dead Reckoning 0 0c eee eee eee 5 31 TIME ZONES verorden imaia Eae a wad ache bie hic Ane eke elena 5 36 Time Notation ccc eee 5 38 viii ix Contents GUI Tools An Overview 5 0 ct et eens 6 2 The Complete GUI Environment maptool 63 Starting maptool 2 0 c eee es 63 TheMenus 0 0 cee tee 6 4 The Mouse Tool Buttons 2 00 c eee ee 6 4 Activating GUIs with maptool A Working Example 65 Setting Initial Map Properties 00 0 0 eae 65 Plotting Layered Atlas Data 0000005 6 7 Editing Object Properties aaea 69 Zooming in on a Map Display 2 0005 6 11 Entering Workspace Commands 0 00 00 6 12 Plotting Line Objects 0 cece eee 6 13 Plotting Text Objects 2 eee 6 14 Editing Text Position 0 0 cece eee 6 15 Plotting Tracks and Calculating Surface Distances 6 16 Hiding Mapped Objects 00 c eee eee 6 20 Editing Map Projection and Display Properties 6 22 Selecting Track Waypoints 00 cea eee eae 6 26 Creating a Navigational Track 20000ee 6 26 Displaying a Navigational Track
78. TLAB document Using MATLAB Graphics 2 42 The Geographic Data Structure The Geographic Data Structure In the previous examples all of the map data was in the form of individual variables and had to be displayed using different mapping commands according to the type of data at hand i e line patch matrix text etc The Mapping Toolbox also provides an easy means of displaying extracting and manipulating collections of all types of map objects that have been organized in a specially defined and formatted geographic data structure Note that this structure is different from the map projection structure which defines a map projection along with its mapping properties The geographic data structure contains the information required for the proper display of the graphic object The following table lists the six object types along with their required fields of information fields light line patch regular surface text type e e e e e e tag lat long e e map e mapl egend meshgrat string altitude otherproperty e 2 Displaying Maps 2 44 Some fields may contain empty entries but the fields themselves must exist for the object to be displayed correctly For instance theal titude field can bean empty matrix andother property can bean empty cell array Thet ag field must bea string not equal tothe name of the object type i e line surf
79. User s Guide Version 1 M apping Toolbox For Use with M ATLA B Systems Planning and Analysis Inc Computation Visualization Programming X OD oe 6 How to Contact The MathWorks 508 647 7000 508 647 7001 The MathWorks Inc 24 Prime Park Way Natick MA 01760 1500 http www mat hworks com ftp mathworks com comp soft sys matlab Support mat hworks com Suggest mat hworks com bugs mat hworks com doc mathworks com subscribe mathworks com service mathworks com info mat hworks com Mapping Toolbox User s Guide Phone Fax Mail Web Anonymous FTP server Newsgroup Technical support Product enhancement suggestions Bug reports Documentation error reports Subscribing user registration Order status license renewals passcodes Sales pricing and general information COPYRIGHT 1997 by The MathWorks Inc All Rights Reserved The software described in this document is furnished under a license agreement The software may be used or copied only under the terms of the license agreement No part of this manual may be photocopied or repro duced in any form without prior written consent from The MathWorks Inc U S GOVERNMENT If Licensee is acquiring the software on behalf of any unit or agency of the U S Government the following shall apply a for units of the Department of Defense RESTRICTED RIGHTS LEGEND Use duplication or disclosure by the Government is subject to restric t
80. Vector Data 00 ccs 7 3 The Digital Chart of the World 02000 7 3 U S Vector Data nananana anaana 7 14 PGE RY LAINE ei smiaran sec Roe et a do tedle le ashesis GaN S i 7 14 TIGER Thinned Boundary 000 cee eee ees 7 18 Global Gridded Elevation Data 7 23 ETOPOS5 and TerrainBase 0000 cece eee ee eee 7 23 Digital Chart of the World DEMS 00000 00a 7 28 U S Gridded Elevation Data 0 0 00 cece eee 7 32 Astronomical Data 0 0 00 c eee eee 7 36 7 External Data Interface 7 2 Working With External Data While the Mapping Toolbox atlas data described in Chapter 3 is suitable for world or regional maps more detailed data is usually required for smaller scale maps The best sources of such data are often national mapping agencies who make their data available to the public at little or no charge often over the Internet or on CD ROM United States government publications are generally free of copyright allowing free re use of the data Although the Mapping Toolbox can easily display such geographic data once it isin the MATLAB environment importing it is often difficult because of complicated data file formats To make these detailed datasets readily accessible The Mapping Toolbox provides a number of external data interface functions These functions allow you to read the data into Mapping Toolbox data types such as re
81. a FLineWidth 3 MapProj ection eqdcylin getm gca FLineWidth ans 3 getm gca MapProjection ans eqdcylin 2 6 Accessing and M anipulating Map Axes Properties Toinspect the entire set of map axes properties at their current settings use the following command get m gca ans mapproj ection angl eunits aspect fixedorient gl i newi ml ine pline geoid mapl atlimit maplonlimit mapparallels nparallels origin trimat triml on frame ffill fedgecolor ffacecolor flatlimit flinewidth flonlimit grid galtitude gcolor glinestyle dth ml ineexcepti on mlinefill mlinelimit ocation mlinevisi ble plineexcepti on plinefill plinelimit ocation plinevisi ble fontangle eqdcylin degrees normal 1 0 90 90 180 180 30 0 0 0 90 90 180 180 To 100 0 0 0 none 90 90 3 180 180 ott Inf 0 0 0 0 5000 100 30 on 100 15 on normal 2 Displaying Maps 2 8 fontco fontn fonts fontun font wei label for labelun meridianla ml abellocat ml abel para ml abel ro parallella plabellocat plabel merid plabelro or ame ize its ght mat bits bel ion el und bel ion ian und 0 0 0 hel vetica 9 points nor mal compass degrees off 30 90 0 aff 15 180 0 Accessing and M anipulating Map
82. a fix or running fix is obtained e DR three hours ahead or for the next three expected fixes e DR for every line of position LOP either visual or celestial 5 32 Navigation For example the navigator plots these DRs DRTime Reason 1400 Hour 1416 Course change 1500 Hour ll 1523 Line of Position visual 1600 Hour l 1634 Fix alv 1700 Hour O jis Doa Fix 1634 l c 090 1700 etc OFS 1500 1523 1600 1634 IEN Ca la Ca Notice that the 1523 DR does not coincide with the LOP at 1523 Although note is taken of this variance one line is insufficient to calculate a new fix The Mapping Toolbox includes the function dr eckon which calculates the DR positions for a given set of courses and speeds The function provides DR positions for the first three rules of dead reckoning The approach is to provide a set of waypoints in navigational track format corresponding to the plan of intended movement The time of the initial waypoint or fix is also needed as well as the speeds to be employed along each leg Alternatively a set of speeds and the times for which each speed will apply can be provided dr eckon will return the positions and times required of these DRs e dreckon calculates the times for positions of each course change which will occur at the waypoints e dreckon calculates the positions for each whole hour e if times are provided for speed changes dr eckon calculates positions for these t
83. ace text etc For complete descriptions of these fields and the object types consult the geographic data structure reference pagein theMapping T ool box Reference Guide Theusal o workspace contains several variables in the geographic data structure format load usalo conus conus lat 4392x1 double long 4392x1 double type patch tag Continental UnitedStates otherproperty altitude stateborder stateborder lat 2345x1 double long 2345x1 double type line tag StateBorder otherproperty 1x1 cell altitude greatlakes greatlakes 1x3 struct array with fields type tag lat long altitude otherproperty The Geographic Data Structure The structureconus contains a patch object of the continental U S greatlakes consists of three patches representing the Great Lakes and the structurestateborder contains line vector data for the state boundaries These can be displayed with the di spl aym function axesm MapProjection lambert MapParallels MaplLatLlLimit 23 52 MapLonLimit 130 62 displ aym conus displ aym greatlakes displaym stateborder The map shown here is virtually identical to that of a previous example in which the vector variablesuslat uslon gtlakelat gtlakelon statelat and statelon were used Now display all 50 states and the District of Columbia using the patches located in the geographic data structure variablestate
84. agged with a name Here are the names of places in the hydrography layer uni que strvcat H tag rows ans Anacostia River Channel Dalecarlia Reservoir Georgetown Reservoir Kenilworth Aquatic Gardens Kingman Lake Lagoon Mc Millan Reservoir Potomac River Reflecting Pool Tidal Basin Washington Channel 7 17 7 External Data Interface The other layers have tags with street names interstate highway numbers railroad names and landmarks names The names can be useful in finding the location of a site or in the selective display of data What is the latitude and longitude of the Washington Monument Mark the spot lat long indx extractm PL washington mon PL indx ans lat 38 8891 long 77 0354 tag Washington Monument type line altitude 0 4000 otherproperty 1x3 cell h displaym PL indx set h Marker x Color r You can also use the mobj ects tool to browse the names of objects that have already been plotted TIGER Thinned Boundary The U S Census Bureau has published lower resolution thinned extracts of the TIGER database in two data file formats ARC INFO and MapInfo Interchange Format MIF ARC INFO and Mapl nfo are geographic information systems GIS developed by the Environmental Systems Research Institute Inc ESRI and MapInfo Corporation respectively Data files for both formats are provided by the U S Census Bureau via the Internet http Awww census gov
85. ale along all great circles from one or two points When the projection is centered on a pole the parallels are spaced in proportion to their true distances along each meridian E quireal projection S E qual area projection Equivalent projection See E qual area projection Flat polar projection A projection on which in normal aspect the pole is shown as a line rather than as a point Frame See Map frame Free of distortion Having no distortion of shape area or linear scale Ona flat map this condition can exist only at certain points or along certain lines General matrix map In the Mapping Toolbox a matrix map defined with latitude longitude coordinate matrices allowing irregular non rectangular orientations Geoid The true shape of the Earth an irregular and complex shape which is usually modeled with a sphere or an ellipsoid In the Mapping Toolbox this term refers to the spherical or ellipsoidal model of the Earth or other planet in use rather than the true shape Geoid vector n the Mapping Toolbox a vector describing the geoid or ellipsoid model The geoid vector has the form geoidvec semi major axis eccentricity Geometric projection S Perspective projection Geographic data structure In the Mapping Toolbox A MATLAB data structure containing the data and other information for the proper display of map objects Valid fields in the structureincludet ype tag andaltitude GIS Geograp
86. als Geographic Interpretations The Mapping Toolbox supports several different interpretations of general matrix maps First a map matrix having the same size as the latitude and longitude coordinate matrices represents the values of the map data at the corresponding geographic points Next a map matrix having one fewer row and column than the geographic coordinate matrices represents the values of the map data within the area formed by the four adjacent latitudes and longitudes Finally if the latitude and longitude matrices are still smaller than the map matrix you can interpret them as describing a coarse graticule or mesh of latitude and longitude cells into which the blocks of map data are warped This section discusses the first two interpretations of general matrix maps Chapter 2 Displaying M aps has more information on the use of graticules As an example of the first interpretation consider a 4 by 4 map matrix whose cell size is 30 by 30 degrees along with its corresponding 4 by 4 latitude and longitude matrices mp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 lat 30 30 30 30 0 0 0 OF ae 30 30 30 30 60 60 60 60 long 0 30 60 90 0 30 60 90 0 30 60 90 0 30 60 90 1 56 W orking with M atrix Maps This general matrix map is displayed with the values of map shown at the associated latitudes and longitudes g 80 150 120 90 60 30 O 30 60
87. an area covering at least 5 or 10 degrees of latitude and longitude but less than a hemisphere Regular aspect See Normal aspect Regular matrix map In the Mapping Toolbox an equiangular equal angle matrix map defined with a map legend vector limited to a rectangular orientation Retroazimuthal projection A projection on which the direction or azimuth from every point on the map to a given central point is shown correctly with respect to a vertical line parallel to the central meridian The reverse of an azimuthal projection Rhumb line A complex curve a spherical helix on a planet s surface that crosses every meridian at the same oblique angle a navigator can proceed between any two points along arhumb line by maintaining a constant heading A rhumb lineis a straight line on the Mercator projection Also called a loxodrome Scale The ratio of the distance on a map or globe to the corresponding distance on the Earth usually stated in the form 1 5 000 000 for example Scale factor The ratio of the scale at a particular location and direction ona map to the stated scale of the map At a standard parallel or other standard line the scale factor is 1 0 A 12 G lossary Secant cone cylinder or plane A secant cone or cylinder intersects the sphere or ellipsoid along two separate lines theselines are parallels of latitude if the axes of the geometric figures coincide A secant plane intersects the sphere or el
88. and longitude 1 30 K korea workspace 2 36 L labels meridians and parallels 2 17 text 2 22 latitude and longitude interpolation 1 30 See also map frame setting limits See also map limits latitude defined 1 7 legs course and distance of 5 30 defined 5 13 legs 5 12 5 30 light objects displaying 2 40 i ght m 2 40 i mi t m 1 44 line objects displaying 2 24 plotting from mapt ool 6 13 6 24 oadcape 3 28 logical maps 1 5 Index 1 6 calculating surface area 1 51 defined 1 51 longitude converting between ranges 1 8 longitude defined 1 8 loxodromes Seerhumb lines ltl n2val 1 47 M map axes accessing properties 2 6 current values 2 7 default values 2 9 defined 2 3 defining a map projection 2 3 differences from standard axes 2 5 resetting to default properties 2 21 setting properties 2 3 2 6 map definition 1 2 map frame adjusting for a new projection 2 19 controlling appearance 2 14 defined 2 11 displaying 2 11 resetting altitude 2 14 setting limits 2 12 2 18 6 22 using mapt ool 6 30 map grid controlling appearance 2 15 defined 2 15 displaying 2 15 resetting altitude 2 15 setting properties 6 6 6 22 using mapt oo 6 30 map layers plotting 6 7 map legend defined 1 43 map limits adjusting for a new projection 2 19 setting 2 13 2 18 versus frame limits 2 18 map projection aspect 4 7 azimuthal 4 6 base 4 13 central 4 6 choosing 4 22 conformal 4 3 conic 4 5 cy
89. ap contains integer country codes By calling the function tI n2val we extracted the country code of the geographic point The country code is an index into the nations structure which returns the name of the country The coarseness of this dataset imposes some limitations J ust like any other matrix entry the coastline and borders between nations are one degree quadrangles that may cover more than 100 kilometers on a side The code for a border is often returned when you query areas with small nations The actual shape of small countries is also poorly represented by such large cells F or instance the area represented by the map in thecape MAT file would cover just 9 cells for this dataset W orld M atrix Data Terrain A low resolution set of global elevation data is provided with MATLAB in the topo workspace It is a regular matrix of average elevations and depths in meters for a constant grid spacing of one degree by one degree load topo whos Name Size Bytes Class topo 180x360 518400 double array topol egend 1x3 24 double array topomapl 64x3 1536 double array topomap2 128x3 3072 double array Hereit is displayed in an equal area Eckert IV projection as a shaded relief surface which allows both large and small features to be seen axesm eckert 4 meshl srm topo topol egend 3 17 3 Atlas Data United States Vector Data Low Resolution Data Vector political and coastline data for the United States are pr
90. ap projection structure for a Sinusoidal projection change the map origin and fill in the rest of the structure fields with default property values J ust as you can change the property settings of a map axes with s et m you can use the entries of the map projection structure to control the projection properties mstruct defaultm sinusoid mstruct origin 0 180 0 mstruct defaultm sinusoid mstruct 4 19 4 M ap Projections Having defined the map projection parameters you can project the latitude and longitude vectors into the proper coordinates of the Sinusoidal projection and display the result using non mapping MATLAB commands x y mfwdtran mstruct lat long line plot x y axis equal set gca XLim 3 5 3 5 YLim 2 2 1 5 5 For the transformation function an empty matrix is used to take the place of altitude data and the string ine identifies the object type and allows the vector data to be clipped and trimmed Notice that the International Date Line is now at the center of the map 180 as specified earlier 4 20 Projection Computations You can transform the projected x y data back into the Greenwich geographic coordinates with the inverse transformation function Plot the result lat2 long2 minvtran mstruct x y plot long2 lat2 axis equal set gca XLim 200 200 YLim 100 100 100 T T T T 807 60 40 20 oF 20 40 L
91. aphic observations Thehi str command results in equirectangular binning Each bin has the same angular measurement in both latitude and longitude with a default measurement of 1 degree The center latitudes and longitudes of the bins are returned as well as the number of observations per bin binlat binlon num histr lats lons As previously noted these equirectangular bins result in counting bias towards the Equator Hereis a display of the one degree by one degree binning of approximately 5 000 random data points in Russia The relative size of the circles indicates the number of observations per bin This is a portion of the whole map displayed in an equal area Bonne projection The first step in creating data displays without area bias is to choose an equal area projection The proportionally sized symbols are a result of the specialized display function scatt erm G eostatistics The area bias can be eliminated by adding a fourth output argument tohi str which will be used to weight each bin s observation by that bin s area binlat binl on num wnum histr lats lons The fourth output is the weighted observation count Each bin s observation count is divided by its normalized area Therefore a high latitude bin will have a larger weighted number than a low latitude bin with the same number of actual observations The same data and bins look much different when they are area weighted Notice that there
92. arc second or 1 250 000 scale DEM data The data is derived from the U S Defense Mapping Agency s DTED 1 digital elevation model which itself was derived from cartographic and photographic sources The cartographic sources are maps from the 7 5 minute through 1 degree series 1 24 000 scale through 1 250 000 scale There is no bathymetric data in this DEM Most of the 1 degree digital elevation models have grid spacings of 3 arc seconds in both the latitude and longitude directions Alaska has grid spacings of 6 arc seconds for latitudes between 50 and 70 degrees North and 9 arc seconds for latitudes greater than 70 degrees North The grid for the digital elevation maps is based on the World Geodetic System 1984 WGS 84 Older DE M s were based on WGS 72 Elevations are in meters relative to the National Geodetic Vertical Datum of 1929 NGVD 29 in the continental U S and local mean sea level in Hawaii The specified absolute horizontal accuracy of the DEM is 130 m whilethe specified absolute vertical accuracy is 30m The relative horizontal and vertical accuracies are not specified but should be much better than the absolute accuracies The DEM data files can be retrieved over the Internet from the EROS Data Center s Web site located at http edcwww cr usgs gov or their FTP server at ftp edcftp cr usgs gov The files are available sorted by state and filename or can be selected from an index map Further information on
93. are larger symbols to the north in this display The previous display suggested that the data was relatively uniformly distributed When equal area considerations areincluded it is clear that the data is skewed tothe north In fact the data used is northerly skewed but a simple equirectangular handling failed to demonstrate this 5 9 5 Mapping Applications The hi str command therefore does provide for the display of area weighted data However the actual bins used are of varying areas Remember the one degr ee by one degree bin near a pole is much smaller than its counterpart near the Equator The hi st a command provides for actual equal area bins Converting to an Equal Area Coordinate System Finally on the topic of equal area data handling the actual data itself can be converted to an equal area coordinate system for analysis with other statistical functions It is easy to convert a collection of geographic latitude longitude points to an equal area x y Cartesian coordinate system Thegrn2eqa command applies the same transformation used in calculating the E qual Area Cylindrical projection x y grn2eqa lat 1 on For each Greenwich at ong pair an equal areax y is returned The variables x and y can then be operated on under the equal area assumption using a variety of two dimensional statistical techniques Tools for such analysis can be found in the Statistics Toolbox and elsewhere The results can then be conve
94. ata 0 0 0 0 ccc eee 3 18 Medium Resolution State Outlines 008 3 23 United States Matrix Data 0 00000 eee 3 26 Political 2 0 eee eee 3 26 o at 9 eee ee 3 28 Astronomical Data 0 0000 cece eee 3 30 3 Atlas Data Types of Data The Mapping Toolbox includes a number of datasets for global and regional displays Map data is availablein both vector and matrix format covering the world and the United States The M apping Toolbox also provides astronomical data for simple stellar cartography More detailed data is available over the Internet or on CD ROM and can be imported to MATLAB using the data interface functions described in Chapter 7 External Data Interface W orld Vector Data World Vector Data Coastlines Thecoast MAT file contains a set of vector shorelines intended for global displays in which political boundaries are not required The data is stored in vectors of latitude and longitude consisting of nearly 10 000 points Whilethis a considerable quantity of data it is of very low resolution by cartographic standards load coast whos Name Size Bytes Class lat 9589x1 76712 double array long 9589x1 76712 double array The dataset is in patch format meaning it has polygon segments that return to their starting points and can therefore be usefully displayed using patch commands The polygon segments are separated by NaNs into about 240 faces Th
95. ates formerly called mean sea level 1929 Nominal scale The stated scale at which a map projection is constructed Normal aspect A form of a projection that provides the simplest graticule and calculations It is the polar aspect for azimuthal projections the aspect having a straight Equator for cylindrical and pseudocylindrical projections and the aspect showing straight meridians for conic projections Also called conventional direct or regular aspect Oblique aspect An aspect of a projection on which the axis of the Earth is rotated soit is neither aligned with nor perpendicular to the conceptual axis of the map projection Orthoapsidal projection A projection on which the surface of the Earth taken as a sphere is transformed onto a solid other than the sphere and then projected orthographically and obliquely onto a plane for the map Orthographic projection A specific azimuthal projection or a type of projection in which the Earth is projected geometrically onto a surface by means of parallel projection lines Orthomorphic projection See Conformal projection Parallel A small circle on the surface of the Earth formed by the intersection of the surface of the reference sphere or ellipsoid with a plane parallel tothe plane of the E quator This lineis identified by its latitude The E quator a great circle is usually also treated as a parallel A 10 G lossary Parallel of opposite sign A parallel that
96. by using two seeds Enter a 2 in the of Seeds box and a4 in the Value box 6 35 6 Gu Tools Press Get and thecross hair appears Click in the first region at the upper left of the map Figure No 1 Seed Map Latitude wo ol 130 140 145 135 Longitude of Seeds EE Yal ue From To E 30 25 6 36 Constructing Personalized Map Data with G Uls For the second seed click inside Sakhalin Island Figure No 1 Seed Map oe 22 a be T w 25 125 130 135 140 Longitude mn of Seeds mej Value Press Fill In and the values corresponding to those two regions will be changed to 4 The last region you need to encode is the small Kuril island that appears to the east of Hokkaido in the upper right corner of the map 6 37 6 Gu Tools Drag the zoom box over the island and double click to Zoom in J Figure No 1 Seed Map BE par 143 ee ee 146 dda 14B ngiku T ca of Seeds Value Because the island is so small and much of its shape consists of coastline this zoomed in view will makeit much easier to select the interior of the island rather than its coast From this view you can also see that you missed a spot on Sakhalin Island see mouse pointer in the picture above so you will need two seeds for this step 6 38 Constructing Personalized Map Data wi
97. ca Asia Europe North America and South America are currently available Samples of J apan Madagascar and Haiti may also be available The Mapping Toolbox interface to DCW DEM files is thedc wdem function It reads the elevations into regular matrix maps optionally downsampling and trimming data in the process 7 28 G lobal Gridded Elevation Data The following examples make use of the Haiti sample files haiti hdr and haiti bil which are available from the EROS Data Center s FTP server at ftp edcftp cr usgs gov or The MathWorks at ftp ftp mathworks com Read the entire Haiti dataset at one fourth resolution Large negative values in the map represent a lack of data rather than actual depth and have been changed to an appropriate value Elevations are given in feet above mean sea level using WGS 84 as a horizontal datum map maplegend dcwdem haiti 4 map map lt 0 1 whos Name Size Bytes Class ma p 121x331 320408 double array mapl egend 1x3 24 double array axesm mercator meshm map mapl egend size map map demcmap map lightm 19 69 5 material 7 7 1 5 lighting gouraud 7 29 7 External Data Interface You can read a subset of the data by providing latitude and longitude limits Hereis the part of the Haiti dataset covering Puerto Rico at the full resolution 30 arc seconds map maplegend dcwdem haiti 1 17 75 18 75 67 5 65 05 map map lt 0
98. ca MapProjection sinusoid showaxes grid off 2 1 57 1b 0 57 OF 0 5 F Similarly vector and matrix data can be displayed using either mapping or standard commands 2 23 2 Displaying Maps Displaying Vector Maps as Lines The Mapping Toolbox lets you display vector map data as line objects much like the line display commands in MATLAB The Mapping Toolbox line graphics functions have MATLAB analogs the names of which can usually be determined by appending an m to the MATLAB function name For instance the Mapping Toolbox version of pl ot iSplotm The following table lists the available Mapping Toolbox line display functions Function Used to Create contorm Contour plot of map data contor3m Contour plot of map data in 3 D space linem Line objects projected on map axes plotm Lines projected on map axes plot3m Lines projected on map axes in 3 D space Plot thecoast vector data using p ot m J ust as with pl ot you can specify line property names and values in the command load coast axesm mol weid framem FEdgeColor blue FLineWidth 0 5 plotm lat long LineWidth 1 Color blue Sometimes vector data represent specific points Suppose you have variables representing the locations of Cairo 30 N 32 E Rio de J aneiro 23 S 43 W and Perth 32 S 116 E and you want to plot them as markers only without connecting line segments 2 24 Displaying Vector M aps a
99. cases there may be times when you need access to the non geographic coordinates of your map data in the projected space An easy way to retrieve the projected coordinates of a map that has already been displayed is with the MATLAB get command The projected coordinates are stored in the object s xdat a andydat a properties As an example display a map frame for the Mollweide projection and extract its x y coordinates axesm mol wei d h framem x get h XData y get h YData Of course you do not need to display a map object to get its projected coordinates You can perform the same projection computations that are done within the Mapping Toolbox display commands Begin by displaying a map of thecoast vector data figure load coast plot long lat axis equal set gca XLim 200 200 YLim 100 100 Projection Computations Hereis the result Note that some of the data extends beyond 180 longitude 100 80 60 40 20 oF 20 40 60 L 80 L 100 L L L L L 200 150 100 50 0 50 100 150 200 Before projecting the data you must define the projection parameters just as you would prepare a map axes with axes m before displaying a map The projection parameters are stored in a map projection structure that normally resides in the Us er Dat a property of a MATLAB axes but you can use it directly for the projection computation The following commands create an empty m
100. cation 1 MLineLocation 1 PLabelLocation 1 PLineLocation 1 GLineStyle GAltitude inf gridm mabel plabel meshm map mapl egend demcmap map 72 69 TRAN 69 W 43 N 42 N 41 N 7 27 7 External Data Interface Digital Chart of the World DEMs Another source of gridded elevation data is the collection of DE Ms derived from the Digital Chart of the World DCW commonly referred toas the DCW DEM The Mapping Toolbox provides an interface to both the DCW and the DEMs derived from it See the section entitled Global Vector Data for more information on the DCW The DCW DEM is currently under development by the Earth Resources Observation Systems EROS Data Center The elevations are computed for a regular grid using the ANUDEM computer program from the Australian National University This program combines elevation and drainage lines and points to interpolate elevations at the grid locations The dataset provides global coverage of land elevations at a horizontal resolution of 30 arc second about 1 kilometer or better The DCW is based on aeronautical charts hence no bathymetric data is available The DCW DEM is accessible over the Internet and can be purchased on CD ROM as major geographic regions are completed Ordering information as well as the actual data files can be found at the EROS Data Center s home page at http edcwww cr usgs gov Preliminary versions of Africa Antarcti
101. ce along a parallel of a point from a given meridian Developable surface A simple geometric form capable of being flattened without stretching Many map projections can be grouped by a particular developable surface cylinder cone or plane Direct aspect See Normal aspect Distortion A variation of the area or linear scale on a map from that indicated by the stated map scale or the variation of a shape or angle on a map from the corresponding shape or angle on the Earth DMS Degrees minutes seconds angle notation of the form ddd mm ss There are 60 seconds in a minute and 60 minutes in a degree In the Mapping Toolbox when dms angles are represented by a single number the format is dddmm ss Ellipsoid When used to represent the Earth a solid geometric figure formed by rotating an ellipse about its minor shorter axis Also called spheroid E qual area projection A projection on which the areas of all regions are shown in the same proportion to their true areas Shapes may be greatly distorted Also called an equivalent or authalic projection A Geographic Terms Equatorial aspect An aspect of an azimuthal projection on which the center of projection or origin is some point along the Equator For cylindrical and pseudocylindrical projections this aspect is usually called conventional direct normal or regular rather than equatorial E quidistant projection A projection that maintains constant sc
102. cell value map row col value 2 More often the geographic coordinates are known value tl n2val map mapl egend lat long value 2 1 47 I apping Fundamentals The latitude longitude coordinates associated with particular values in a matrix map can be found withf i ndm which is similar tothe standard MATLAB command f i nd Here we find the coordinates in thet opo map with values greater than 5500 meters load topo lats longs findm topo gt 5500 topolegend lats longs ans 34 5000 79 5000 34 5000 80 5000 30 5000 84 5000 28 5000 86 5000 You can change all instances of a given valuein a matrix map toa new value in one step Here is an example using the map of Russia oldcode Itln2val map mapl egend 37 79 oldcode 4 newmap changem map 5 ol dcode newcode Itln2val newmap mapl egend 37 79 newcode 5 All entries in newmap corresponding to 4s in map now have the value 5 You can also definea mask to determine map entries to change A mask is a matrix the same size as the map matrix with 1s everywhere the entry is to take on the new value A mask is often generated by a logical operation on a map variable a topic which is described in greater detail below The map in ther ussi a workspace contains 3s for Russia If you want to set every non Russia matrix entry to zero you can use mas k m nonrussia map 3 newmap maskm map nonrussia 0 newcode Iti n2val newmap
103. ction for the version of the database contained in the two text files etopo5 southern bat and etopo5 northern bat These files occupy about 60 megabytes of total disk space when uncompressed and are provided via FTP by the U S Geological Survey at ftp ftp walrus wr usgs gov and by The MathWorks Inc at ftp ftp mathworks com ETOPOS has been superseded by TerrainBase which is similar in coverageto ETOPO5 but corrects many of its flaws including discontinuities at joins between datasets systematic shifts in location and lack of data in some regions TerrainBase is a compilation of the best available public domain data from almost 20 different sources including ETOPO5 and DCW DEM another digital elevation model that has a Mapping Toolbox interface covered in the next section 7 23 7 External Data Interface TheT errainBase dataset was created by the National Geophysical Data Center and World Data Center A for Solid Earth Geophysics in Boulder Colorado The model is currently under development and will be updated as new data sources become available Further information on the TerrainBase DEM can be found at the U S National Geophysical Data Center home page at http Awww ngdc noaa gov TerrainBase data is read usingthet base function The data files are available on CD ROM and vial nternet NOAA NGDC provides ordering information and downloadable files at their Web site The files require about 18 megabyt
104. d general matrix maps in a variety of formats Recall that regular matrix maps require a map legend vector that describes the scale and location of the map while general matrix maps require matrices of latitude and longitude coordinates The matrix map display functions are geographic analogies to the MATLAB surface drawing commands Like the line plotting functions discussed in the previous chapter the Mapping Toolbox function names are usually identical to their MATLAB counterparts except for the addition of an m For instance the Mapping Toolbox functions surf acem and surf m are analogous to MATLAB s surface andsurf commands You will most likely find a Mapping Toolbox version of a MATLAB surface drawing function by appending an m to the MATLAB function name NOTE In the Mapping Toolbox the set of functions beginning with mesh are used for regular matrix maps while those with surf are reserved for general matrix maps It should be noted here that this usage differs entirely from MATLAB s definition that is mesh plots are used for colored wire frame views of the surface whilesurf displays colored faceted surfaces Surface map objects can be displayed in a variety of different ways You can assign colors from the figure colormap to surfaces according to the value of their data You can also display images where the matrix data consists of indices into a colormap or display the matrix as a three dimensio
105. d showaxes off is executed to remove axes ticks from the MATLAB Cartesian axes i e thexTick YTi ck andZTi ck properties are set to empty matrices More information on MATLAB axes properties can be found in the Using MATLAB Graphics manual under Axes The map axes properties are defined under the axes m heading in the Mapping Reference chapter in the Mapping Toolbox Reference Guide while information on the use of theaxesm GUI can be found in the GUI Reference chapter in the Mapping Toolbox Reference Guide 2 Displaying Maps Accessing and Manipulating Map Axes Properties J ust as the properties of the underlying standard axes can be accessed and manipulated using the MATLAB commandsset and get map axes properties can also be accessed and manipulated using the commands s et m and get m NOTE Use theaxesm command to create a map axes Use thes etm command to modify the map axes As an example create a map axes axesm MapProjection mller Frame on Suppose you would like to make the frame lines bordering the map thicker First you need to determine the current line width of the frame Access the property value by typing getm gca FLineWidth ans 2 Try resetting the line width to four points setmgca FLineWidth 4 You can set any number of properties simultaneously with s et m Reduce the line width change the projection to an Equidistant Cylindrical and verify the changes setm gc
106. dDE fk5 DEd fk5e DEd mRA fk5 RAm fk5e RAm mDE fk5 DEm fk5e DEm SRA fk5 RAS fk5e RAs sDE fk5 DEs fk5e DEs lat dms2deg dDE mDE sDE lon hms2hr hRA mRA SRA 360 24 You probably want the map to look like you are inside the celestial sohere looking out so switch the sign of the longitudes lon zero22pi lon It is customary to display the stars with sizes proportional to the visual magnitudes Extract the magnitudes from the data structures magn fk5 Vmag fk5e Vmag Faint stars have large visual magnitude numbers while bright ones have smaller values The magnitudes of particular bright stars were used to define the visual magnitude scale It was later determined that certain stars were even brighter than the reference stars resulting in negative visual magnitudes You will need to convert the values to positive numbers for plotting pyvmag 0 01 max magn magn clear fk5 fk5e 7 38 Astronomical Data Stars in equatorial coordinates are typically displayed in the Equidistant Azimuthal projection Here is the southern sky You can see the southern cross at about 60 S 175 E axesm eqdazim framem gridm mlabel plabel setmgca Origin 90 180 0 FLatLimit inf 90 MLineLocation 15 MLabelLocation 180 15 165 MLabel Parallel equator MLineLimit 75 75 PLabel Location 15 15 75 GLineWidth 01 GLineStyle scattermlat lon p
107. dive ee be ease ee Pew die 1 4 Composite MapS 0 00 aaea 1 6 Geographic Measurement 0020000 1 7 Latitude and Longitude 0 0 cece eee 1 7 Great Circles and Rhumb Lines 00 0c eee 1 9 Measuring Distance 00 eee 1 10 Measuring Azimuth 0 00 e eee 1 11 Reckoning Positions 0 00 c cece ees 1 13 Small Circles vseGas68seerus ee ode p44 eee hes PERO eS 1 13 Measuring Area ee tees 1 15 The Geoid Model 0 0 c eects 1 16 Measuring the Planets 0 002 cece eee eee 1 19 Angles Times and Distances Units and Notation 1 21 Angular Notation 0 000 c eee eee 1 21 Time Notation 0 0 0 ee 1 23 Distance Notation eaaa 1 24 Working with Vector Maps 0 005 1 25 Data FO MAE restrito riet new ee eed Whee eae de eta 1 25 Segments versus Polygons 0 0c eee eee eee 1 26 Creating Vector Data 0 cee eee 1 27 Geographic Interpolation 0 00 cee eee 1 30 Polygon Area o rera heera ea ai a eee 1 32 Vector Calculations Intersections unana 1 34 Trimming Vector Data to a Defined Region 1 36 Simplifying Vector Data s saaa 1 38 Working with Matrix Maps 45 1 42 Regular Matrix Maps 00 0 aaea 1 42 General Matrix Maps 0 00 a 1 53 I apping Fundamentals What Is a Map The simplest definition of a map is a repre
108. duce geoid heights from oceanic regions between 70 north and south latitude Geoid heights were also deduced from ground based Doppler and ground based laser satellite tracking data as well as surface gravity data Zenithal projection See Azimuthal projection A 15 A G eographic Terms A 16 Bibliography B Bibliography 1 Snyder J P Map Projections A Working Manual U S Geological Survey Professional Paper 1395 Washington D C 1987 2 Maling D H Coordinate Systems and Map Projections 2nd Edition Pergamon Press New York NY 1992 3 Snyder J P and Voxland P M An Album of Map Projections U S Geological Survey Professional Paper 1453 Washington D C 1994 4 Snynder J P Flattening the Earth 2000 Y ears of Map Projections University of Chicago Press Chicago IL 1993 A almanac 1 19 almanac data 1 19 angle units convention for navigation functions 5 12 converting between formats 1 22 description of formats 1 21 angl edi m 1 23 anti pode 1 9 areaint 1 32 areamat 1 51 areaquad 1 15 aspect See projection aspect astronomical data 3 30 axes Seemap axes axes2ecc 1 17 axesm 2 3 2 11 2 15 azimuth defined 1 11 measuring 1 11 azimuth 1 11 azimuthal projection 4 6 B base projection 4 13 bearing Seeazimuth C cape workspace 3 28 central projection 4 6 changem 1 48 choropleth maps example 2 52 circles Se great circles See small circles Click and drag editor 6 15 coa
109. e difference between the semimajor and semiminor axes of a correct ellipse at this scale would be far smaller than the width of the line used to draw it What Is the Correct Geoid Vector A variety of ellipsoid models have been proposed through the years They differ because of the surveying information upon which they are based or because certain regions of interest of the true geoid are best modeled by a particular ellipsoid that may be less accurate for other parts of the world The Mapping Toolbox default geoid vector after the sphere is based on the 1980 Geodetic Reference System ellipsoid This geoid vector is returned by the statement almanac earth geoid Itis alsothe reference ellipsoid for the 1984 World Geodetic System equipotential model Several other geoid vectors are supported for models ranging from E verest s 1830 ellipsoid used for India to the International Astronomical Union ellipsoid of 1965 used for Australia These can be referenced by the following statements geoidl geoid2 almanac earth geoid almanac earth geoid everest iau65 i iC The reference page for thea manac function has more information on which geoids are available Geographic M easurement You should probably use a spherical Earth unless you have a good reason to use an ellipsoidal model If you use an ellipsoidal model you should probably use the default unless you need a specific one If you cann
110. e 1 5373 hours after midnight or 1 32 a m at time 0132 in navigational time format What time would you reach the rendezvous if you increased your speed to 7 knots at 1 15 a m 0115 or 1 25 hours after midnight Toindicatetimes for speed changes another input is required providinga time interval after the fix time at which each ordered speed isto end The first speed 5 knots is to end 1 25 hours after midnight Since you don t know when the rendezvous will be made under these circumstances set the time for the second speed 7 knots to end at infinity No DRs will be returned past the last waypoint spdti mes 1 25 inf drlat drlon drtime drlat drlon drti me ans 10 10 10 10 10 0000 0000 0000 0570 1001 Co Co Oo CO 0846 1058 0d 1586 1801 dreckon waypoints fixtime Speeds spdtimes 0000 2500 4552 0000 4113 Position at 1 am Position at speed change Time of course change Position at 2 am Time at final waypoint 5 35 5 Mapping Applications 5 36 This following illustration shows the difference Time at 10 1 N 0 18 E is 2 4113 q Position at es 2 0 10 057 N 0 159 E Fix at midnight 10 N 0 at time 0 0 given m m COI Time of turn at S7 Pa s 10 N 0 13 E is 1 4552 Position y time 1 0 10N 0 085 E p unchanged Position at 1 25 s speee change ON 0 1058 E
111. e data can also be displayed as lines or points axesm giso framem gridm patchesmlat long FaceColor 0 75 1 1 1 3 Atlas Data 3 4 The resolution for this dataset makes it ideal for global scale displays but inappropriate for significantly smaller regions as can be seen when the region around Cape Cod in the northeastern United States is displayed This is incidentally the area covered by thecape MAT file provided with MATLAB figure axesm MapProjection mercator MapLatLimit 41 44 MapLonLimit 72 69 framem gridm MLineLocation 1 PLineLocation 1 mlabel MLabel Location 1 plabel PLabelLocation 1 patchesm lat long FaceColor 75 1 1 1 W orld Vector Data World Atlas Data The global atlas data contains a set of very small scale approximately 1 30 000 000 data for usein global displays The data is provided in the form of Mapping Toolbox geographic data structures containing national boundaries rivers lakes and cities Hereis a list of the structures in the wor dl o workspace load worldlo whos Name Size Bytes Class DNl ine 1x2 112546 Struct array DNpatch 1x39 59884 Struct array POline 1x2 456600 struct array POpatch 1x206 682454 Struct array POtext 1x194 188132 Struct array PPpoi nt 1x319 400426 Struct array PPtext 1x318 296988 Struct array description 4x75 600 char array gazette 1x513 353504 Struct array The data has been classified into Drainage DN Po
112. e is the zoomed in region of Cape Cod The level of detail is noticeably greater than that for the data in theusal o MAT file 447 70 W 69 W 43 42 41 3 25 3 Atlas Data United States Matrix Data Political The Mapping Toolbox also provides a set of political matrix data for the continental United States located in theus amt x MAT File load usamt x whos Name Size Bytes Class cl r map 54x3 1296 double array map 140x370 414400 double array mapl egend 1x3 24 double array States 54x15 1620 char array The data is in a regular matrix map format similar to that discussed in the section World Matrix Data The variable map is at a resolution of 5 cells per degree or roughly 20 kilometers or better Recall that the resolution of the worl dmtx data is 1 cell per degree hence this dataset is five times finer A colormap has been provided along with a vector of state names both corresponding to the political code or index used in the map matrix Display the matrix map in an Albers E qual Area Conic projection axesm MapProjection eqaconic MapParallels MapLatLimit 24 52 MapLonLimit 134 60 MLabelLocation 15 MLineLocation 15 PLabelLocation 15 PLineLocation 15 GColor 5 1 1 1 GLinestyle MLabel Parallel south framem gridm mlabel plabel meshm map mapl egend col ormap clrmap 3 26 United States M atrix Data Hereis the res
113. ear the frame limits boxes and press the Default button to recalculate the frame limits for the current entries The Projection Control dialog box should now appear as follows Projection Control Map Projection Cyln Mercator Cylindrical Y Angle Units Map Limits Frame Limits Latitude s Latitude 36 Longitude Longitude 12 5 Map Origin Parallels o Lat and Long O T F Orientation o Aspect nor mal ka Press the Grid button to bring up the Map Grid Properties dialog box Press Meridian and Parallel Settings and change the longitude and latitude locations of the grid lines to 5 Press Accept to return to the Map Grid Properties and then press Accept to return to the Projection Control box 6 22 The Complete GUI Environment maptool Press Apply to re project the map with the new settings Note how the parts of the map outside the limits you specified are now automatically trimmed E im Zoom Rotate Origin O ae ee ae a ee y S w aa a 4 AN ie EE T as l i iS NI fi i 4 coat el aon ake es For more information on using the Projection Control box to edit map projection and display properties see the descriptions for axesm axesmui in the GUI Reference section of the Mapping Tool box Reference Guide To plot city markers and labels as you
114. ece of the Earth The entries of an indexed map answer the question What is this To illustrate the difference between valued maps and indexed maps consider two geographic points 45 N 105 E and 47 N 108 E The valued map t 0 po contains a different kind of information for these points from what is found in the indexed world map load topo ltl n2val topo topolegend 45 105 1270 ltl n2val topo topol egend 47 108 ans 1513 As might be expected the two regions represented by the appropriate entries of topo have different average elevation values However they have the same index value in map because they are in the same country load worl dmt x tl n2val map maplegend 45 105 ans 119 ltl n2val map mapl egend 47 108 ans 119 nations 119 name ans Mongolia 1 50 W orking with M atrix Maps Matrix Maps as Logical Variables A powerful use of matrix maps is the application of logical conditions to create logical maps Logical maps are matrix maps consisting entirely of 1s and Os They can be created by performing logical tests on matrix map variables The resulting binary matrix is the same size as the original map s and can use the same map legend as the following illustrates logical map real map gt 0 Multiple conditions can operate on the same map logical map real map gt 100 amp real map lt 100 Or if several maps are the same size and share the same map legend
115. eds are always in knots nautical miles per hour The functions for which these conventions hold aredreckon gcwaypts egs and navfix Related functions that do not carry this restriction includer hxrh SCXSC gCXgc gcxsc track timezone andcrossfi x becauseof their potential for application outside of navigation Navigation Navigational Track Format Navigational track format requires column vector variables for the latitudes and longitudes of track waypoints A waypoint is a point through which a track passes usually corresponding to a course or speed change Navigational tracks are made up of the line segments connecting these waypoints which are called legs In this format therefore n legs are described using n 1 waypoints because an endpoint for the final leg must be defined waypoint 1 waypoint 6 waypoint 2 waypoint 5 leg 5 waypoint 4 waypoint 3 leg 4 leg 3 Here five track legs require six waypoints In navigational track format the waypoints would be represented by two 6 by 1 vectors one for the latitudes and one for the longitudes Fixing Position The fundamental objective of navigation is to determine at a given moment how to proceed to your destination avoiding hazards on the way The first step in accomplishing this is to establish your current position Early sailors kept within sight of land to facilitate this Today navigation within sight or radar range of land is called p
116. elon k 90 W The structure arrays are Mapping Toolbox geographic data structures and can be displayed using ml ayers ordisplaym Thedatainst at eborder is identical tothatinstatelat andstatel on Similarly conus contains the same outline of the continental United States asus at andus on but is defined to be displayed as a patch The 50 state and District of Columbia patches are located in thestate structure 3 19 3 Atlas Data Display thest ate structure using disp aym Notice the only one command is needed to plot 51 different patches figure axesm MapProjection eqaconic MapParallels MapLatLimit 15 75 MapLonLimit 175 60 MLabelLocation 15 MLineLocation 15 PLabelLocation 15 PLineLocation 15 GColor 5 1 1 1 GLineStyle MLabel Parallel south framem gridm mlabel plabel displaym state colormap summer The states are all tagged allowing them to be manipulated or to be extracted by name You can see the available state names by entering the following strvcat state tag 3 20 United States Vector Data The state of Massachusetts can be displayed by itself or with its neighboring southern states Connecticut and Rhode Island atl longl extractm state mass at2 long2 extractmstate strvcat mass conn rhode igure axesm mercator patchmlat1l long1 0 75 0 figure axesm mercator patchesmlat2 long2 0 75 0
117. entry in the matrix map contains a 1 if it is above sea level or a O if it is at or below sea level G lossary Longitude The angle made by the plane of a meridian passing through a given point on the Earth s surface and the plane of the prime meridian passing through Greenwich England east or west to 180 positive if the point is east negative if it is west One of the two common geographic coordinates of a point on the Earth Loxodrome See Rhumb line Map A representation of geographic data In the Mapping Toolbox a map is any variable or set of variables electronically representing or assigning values to a geographic location or region from a single point to an entire planet Map axes In the Mapping Toolbox a normal MATLAB axes altered for mapping display purposes Several map axes properties are defined and stored intheUser Data slot of the MATLAB axes These properties control the appearance of the map display much like the properties of the normal MATLAB axes control the appearance of the displayed plot A map axes must first be defined in order to display maps using the Mapping Toolbox Map frame In the Mapping Toolbox a projected box or quadrangle enclosing the geographic display Map grid A displayed network of lines representing parallels and meridians The grid is used for visual reference and should not be confused with the graticule Map legend In the Mapping Toolbox a vector defining the g
118. eographic placement and unit cell size of a regular matrix map A map legend has the form maplegend cells angleunit north latitude west longitude MapInfo A largely PC oriented GIS developed and distributed by the Mapl nfo Corporation Matrix map A map consisting of a matrix or matrices of values corresponding to specific geographic points In the Mapping Toolbox matrix maps can be defined as regular or general depending on the structure and orientation of the geographic points See Regular matrix map and General matrix map A Geographic Terms Meridian A reference line on the Earth s surface formed by the intersection of the surface with a plane passing through both poles and some third point on the surface This line is identified by its longitude On the Earth as a sphere this line is half a great circle on the Earth as an ellipsoid it is half an ellipse Minimum error projection A projection having the least possible total error of any projection in the designated classification according to a given mathematical criterion Usually this criterion calls for the minimum sum of squares of deviations of linear scale from true scale throughout the map least squares NGVD 29 National Geodetic Vertical Datum of 1929 A reference surface established by the U S Coast Guard and Geodetic Survey of 1929 used as the datum for which relief features and elevation data are referenced in the conterminous United St
119. er the following in the Workspace Command box tracklat tracklon track waylat waylon Press Apply when done Again the Status Report box appears Press OK The variablestrackl at andtrackl on are now in the workspace For more information on connecting waypoints with track segments see the Mapping Reference section of the Mapping Toolbox Reference Guide 6 26 The Complete GUI Environment maptool Displaying a Navigational Track To plot the tracks select Map gt Lines from the menu bar Entertrack at in the Latitude variable edit box andt rack on inthe Longitude variable edit box In Other Properties enter Tag Navigational Track Color black and press Apply The track appears on your map display E E igure No d ENH Plotting Patches To make your map more colorful you can plot the country patches from the worl dl o workspace usingthemi ayers GUI Select Display gt Projection from the menu bar use the Grid button to turn the grid off then press Apply To plot the patches select Session Layers World LoRes from the menu bar When the worldlo dialog box appears select P Opat ch and press Plot After the country patches have been plotted close the worldlo dialog box 6 27 6 G UI Tools Changing the Stacking Order of Mapped Objects The country patches were plotted in the same z plane as the city markers and labels You can place the
120. erproperty is specified in the geographic data structure W orld Vector Data In the following example it is evident that the many islands of Indonesia and Canada are similarly colored as are all parts of the United States figure axesm mollweid framem gridm displ aym POpat ch You can use the tags to reduce the amount of data in the display by selectively deleting data This can be done by displaying all of the data in a structure and then using the tags to get the handles of the displayed objects you wish to remove The first European example made use of this technique as does the next one It shows rivers lakes and coastlines International boundaries have been removed using their tags cl ma axesm moll weid framem gridm displ aym POI ine delete handlem International Boundary displ aym DNI i ne 3 Atlas Data Here is the map of world coastlines and drainage There area number of other ways to work with the tags associated with this data We can view the tags in the workspace by working directly with the geographic data structure uni que strvcat DNline tag rows ans Inland shorelines Streams rivers channelized rivers Or we can useml ayers and mobj ects to plot the structures view the tags and manipulate similarly tagged objects as a group See Chapter 6 GUI Tools for some examples 3 10 W orld Vector Data The tags can also be used to extract data from the structures
121. es cross is a fix Since you have used only two lines however its quality is questionable Point A Cape Jones Point C Gilligan s Lighthouse Navigation But wait your port lookout says he took a bearing on Cape ones of 300 If that line exactly crosses the point of intersection of the first two lines you will have a perfect fix Point A Cape Jones Point C Gilligan s Lighthouse 1 poor fix lt a Whoops What happened Is your lookout in error Possibly but perhaps one or both of your bearings was slightly in error This happens all the time Which point 1 2 or 3 is correct As far as you know they are all equally valid In practice the little triangle is plotted and the fix position is taken as either the center of the triangle or the vertex closest to a danger like shoal water If the triangle is large the quality is reported as poor or even as nofix If a fourth line of bearing is available it can be plotted to try to resolve the ambiguity When all three lines appear to cross at exactly the same point the quality is reported as excellent or perfect Notice that three lines resulted in three intersection points F our lines would return six intersection points This is a case of combinatorial counting Each intersection corresponds to choosing two lines to intersect from among n lines so the total number of intersection points
122. es of disk space when uncompressed You should use the TerrainBase dataset unless you havea good reason to want ETOPOS TerrainBase corrects some errors takes up less space and can be read faster than ETOPOS5 The following examples will read TerrainBase data but you can substitute ETOPO5 data by simply using theetopo5 function instead of tbase A 10 kilometer resolution DEM has so much data that it is usually impractical to read the entire file into memory The full matrix has 2160 by 4320 elements Both theetopo5 andtbase functions allow you to reduce the resolution by discarding data points Read every twelfth point in the global data base map maplegend tbase 12 whos Name Size Bytes Class map 180x360 518400 double array mapl egend 1x3 24 double array 7 24 G lobal Gridded Elevation Data Plot the map on a Robinson projection axesm robinson meshm map mapl egend demcmap map This is a regular matrix map at the same resolution as thet opo map It differs fromtopo in that the values represent nearest neighbor samples rather than averages over the matrix cell resulting in a rougher appearance Elevations and depths aregiven in meters above or below mean sea level Some parts of the world are represented by data with a horizontal resolution as coarse as 1 degree by 1 degree The vertical resolution varies from 1 meter for Australia and New Zealand to as much as 150 meters for parts of Africa Asia and Sout
123. et opo map flats flons filterm lats lons topo gt 0 topol egend 1 The result would be those points corresponding to land 5 11 5 Mapping Applications 5 12 Navigation One field that makes extensive use of geographic information is navigational science and practice The Mapping Toolbox includes a variety of specialized functions for navigation The practice of navigation includes a variety of tasks for the operation of both watercraft and aircraft One task is establishing position using known fixed landmarks piloting employing the stars Sun and Moon celestial navigation utilizing technological fixing systems radio and satellite navigation including GPS or deducing net movement from a past known position dead reckoning Another navigational task involves planning a voyage or flight which includes determining a short route great circle approximation weather avoidance optimal track routing and setting out a plan of intended movement track laydown The Mapping Toolbox contains functions for some of these navigational activities Conventions for Navigational Functions Units The Mapping Toolbox is in general very flexible in allowing a variety of angular and distance measurement units To make the strictly navigational functions easy to handle and to conform to common navigational practice for these specific functions angles are always in degrees distances are always in nautical miles and spe
124. ether the other two for Erie and Ontario 1 33 I apping Fundamentals Vector Calculations Intersections The Mapping Toolbox provides a set of functions to perform intersection calculations on vector data computed by the toolbox which include great and small circles as well as rhumb line tracks The functions do not however determine intersections of arbitrary vector data Compute the intersection of a small circle centered at 0 0 with a radius of 1250 nautical miles and a small circle centered at 5 N 30 E with a radius of 2500 kilometers lat long scxsc 0 0 nm2deg 1250 5 30 km2deg 2500 lat 17 7487 12 9839 long 11 0624 16 4170 17 7 N 11 1 E 5 N 30 E 2500 km 1250 nm 13 0 S 16 4 E Notice that in general small circles intersect twice or never For the case of exact tangency scxsc returns twoidentical intersection points Other similar commands includerhxrh for intersecting rhumb lines gcxgc for intersecting great circles and gcxsc for intersecting a great circle with a small circle 1 34 W orking with Vector M aps Imagine a ship setting sail from Norfolk Virginia 37 N 76 W maintaining a steady due east course 90 and another ship setting sail from Dakar Senegal 15 N 17 W with a steady northwest course 315 Where would the tracks of the two vessels cross lat long rhxrh 37 76 90 15 17 315 lat 37 long 41 7028 The inte
125. f the stars in this coordinate system are given in the vectors gl at and gl ong Stars in galactic coordinates are typically plotted in a pseudo cylindrical projection like the Mollweide figure axesm mol wei d framem gridm mlabel plabel setmgca FlatLimit inf 90 GLineWdth 01 GLineStyle MLabelParallel equator MLabel Location 120 60 180 MLineLocation 15 scatterm glat glong pvmag MarkerSize 0125 See Chapter 7 External Data Interface for more information on how to convert between these two systems 3 32 Map Projections What Isa Projection 00 e eee eee 4 2 Quantitative Properties 0 c eee eee 4 3 Geometric Surfaces 000 ccc eee 4 4 Projection Aspect 0 0 eee 4 7 The Origin Vector 2 0 0 ce eee 4 7 Coordinate TransformationS 0 0 00 ce eee eee eee 4 14 Projection Computations 0 0048 4 18 Summary Guide 00 0 0 c eee ee 4 22 4 M ap Projections What Is a Projection It has long been established that the shape of the E arth resembles a sphere and not a flat surface If the world wereindeed flat cartography would be a trivial matter and map projections would be quite unnecessary Tocreate a two dimensional representation of a curved surface such as the Earth you must determine how to transform that surface toa plane The
126. following example is for a Macintosh computer so no device name is needed The latitude and longitude limits correspond to the Cape Cod region Struc dcwdata NOAMER 41 44 72 69 line 22 Error using gt dcwdata Theme not present in library NOAMER Valid two letter theme identifiers are PO Political Oceans PP Populated Places LC Land Cover VG Vegetation RD Roads RR Railroads UT Utilities AE Aeronautical DQ Data Quality DN Drainage DS Supplemental Drainage HY Hypsography HS Supplemental Hypsography CL Cultural Landmarks OF Ocean Features PH Physiography TS Transportation Structure 7 6 Global Vector Data Assuming that you are using a Windows PC with the NOAMER CD ROM in the F drive you can read the Political Ocean line features for the same Cape Cod region by entering the following POline dcwdata F NOAMER 41 44 72 69 PO line POline 1x12 struct array with fields type otherproperty altitude lat long tag The result is a Mapping Toolbox geographic data structure Look at the geographic limits by concatenating the data with extract m lat long extractm POIline max lat max long min lat min long ans 45 0003 65 0000 40 0000 75 0000 Notice that this region is larger than was requested The DCW tiles the world into 5 by 5 degree quadrangles When a tile overlaps the requested region dcwdata extracts the data f
127. g T Normal Small Circle 15 from point A g SQ a a a a i Pseudo Small Circle 15 from point C _ in rhumb line sense __ Geographic M easurement Measuring Area In solid geometry the area of a spherical quadrangle can be exactly calculated A spherical quadrangle is the intersection of aluneand a zone In geographic terms a quadrangleis defined as a region bounded by parallels north and south and meridians east and west Quadrangle In the pictured example a quadrangle is formed by the intersection of a zone which is the region bounded by 15 N and 45 N latitudes and a lune which is the region bounded by 0 and 30 E longitude Under the spherical planet assumption the fraction of the entire spherical surface area inscribed in the quadrangle can be calculated area areaquad 15 0 45 30 area 0 0187 1 15 I apping Fundamentals That is less than 2 of the planet s surface area is in this quadrangle To get an absolute figure in for example square miles you must provide the appropriate spherical radius The radius of the Earth is about 3958 9 miles area areaquad 15 0 45 30 3958 9 area 3 6788e 06 The surface area within this quadrangle is over 3 6 million square miles for a spherical Earth The Geoid Model Although the Earth is round it is not exactly a sphere However for many users and most applications the difference is so small that a
128. g straight in one projection will be incorrectly displayed as straight lines in others 1 41 I apping Fundamentals Working with Matrix Maps One of the most powerful features of the Mapping Toolbox is its capacity for manipulating matrix maps Two types of matrix maps are defined by the Mapping Toolbox regular and general Regular matrix maps are rectangular in appearance and area subset of general matrix maps which can be of practically any shape or orientation Regular Matrix Maps A regular matrix map is onein which columns of data run south to north rows of data run west to east and each matrix element represents the same angular step in each direction for all rows and columns For example if each row represents one degree of latitude and each column one degree of longitude and the matrix is aligned north and south then it isa regular matrix map Thet opo map provided with MATLAB is such a regular matrix map 1 42 W orking with M atrix Maps The Map Legend Many regular matrix maps do not cover the entire planet It is therefore necessary to identify the scale and placement of the map with a special data structure the map legend The map legend is a three element vector that identifies the size of each matrix entry and the coordinates on the globe of the northwestern corner of the map The three entries are given in terms of angular units of degrees only The specific format of the structure is as follows
129. gular matrix maps and geographic data structures A wide variety of data is accessible through these external interface functions There are vector map data of political entities ranging from national and local government boundaries infrastructure such as roads railroads airports and utilities and geographic data such as coastlines rivers elevation contours and land use The Earth s surface and ocean elevations are available on regular grids at anumber of different resolutions Astronomical data in the form of star databases is also available Many other types of data can be imported to MATLAB beyond the specialized data file formats accessed by the external interface functions The most important are mapped scientific data in the form of HDF files and J PEG files See the MATLAB documentation for thei mf i nfo andi mr ead functions for more information on how to read these file formats Global Vector Data Global Vector Data The Digital Chart of the World The most detailed publicly available set of global vector data with consistent coverage of important map features is the Digital Chart of the World DCW It contains vector data scanned from printed Operational Navigation Charts ONC and J et Navigation Charts J NC The ONC charts were compiled at a scale of 1 1 000 000 and the NC at 1 2 000 000 The publisher of the DCW was the U S Defense Mapping Agency now incorporated into the U S National Imagery and Mapping Agency
130. h America Oceanographic data in areas shallower that 200 meters contains little detail because of the way depth contours were converted to gridded depths The areas with 1 degree horizontal data can be clearly seen when you display data for a small region at the full resolution of the database 7 25 7 External Data Interface Display the Korean peninsula and J apan map maplegend tbase 1 30 45 115 145 axesm MapProjection polycon MapLatLimit 30 45 MapLonLimit 115 145 MLabelLocation 5 MLineLocation 5 PLabelLocation 5 PLineLocation 5 GLineStyle GAltitude inf gridm mlabel plabel meshm map mapl egend size map map demcmap map lightm 37 5 130 material 7 7 1 5 lighting gouraud 145 E 35 N 30 N Note the discontinuities in some areas particularly the regions in China 7 26 G lobal Gridded Elevation Data You can get a sense for the resolution of this dataset by comparing a TerrainBase map of the Cape Cod region in the Northeastern United States with maps of the same region using other datasets TerrainBase and ETOPO5 havea horizontal resolution of 12 cells per degree so the Cape Cod map consists of 36 by 36 cells map maplegend tbhase 1 41 44 72 69 whos Name Size Bytes Class ma p 36x36 10368 double array mapl egend 1x3 24 double array axesm Mapprojection mercator MapLatLimit 41 44 MapLonLimit MLabel Lo
131. halic projection See E qual area projection Axes See Map axes Azimuth The anglea line makes with a meridian taken clockwise from north Azimuthal projection A projection on which the azimuth or direction from a given central point to any other point is shown correctly When a poleis the central point all meridians are spaced at their true angles and are straight radii of concentric circles that represent the parallels Also called a zenithal projection Bathymetry The measurement of water depths of oceans seas lakes and other bodies of water Bowditch Nathaniel A late 18th early 19th century mathematician astronomer and sailor who wrote the book on navigation J ohn Hamilton Moore s The Practical Navigator was the leading navigational text when Bowditch first went out to sea and had been for many years Early in his first voyage however Bowditch began noticing errors in Moore s book which he recorded and later used in preparing an American edition of M oore s work The revisions were to such an extent that Bowditch was named the principal author and the title was changed to The New American Practical Navigator published in 1802 In 1868 the U S Navy bought the copyright to the book which is still commonly referred to as Bowditch and considered the bible of navigation Cartography The art or practice of making charts or maps Central meridian The meridian passing through the center off a p
132. he appropriate break points F or vector map data the connectivity of the data is often only a concern during display Toillustrate a vector map enter the following load coast whos Name Size Bytes Class lat 9589x1 76712 double array long 9589x1 76712 double array axesm mercator framem plotm lat long The variables at and ong are vectors in thecoast MAT file which together form a vector map of the coastlines of the world They form a map independent of whether they are displayed I apping Fundamentals We have chosen to view the map in a Mercator projection Matrix Maps A matrix in which each element represents a value corresponding to a specific geographic area also forms a map In this case the geographic data is in matrix format which is often called raster format However the Mapping T ool box makes great use of the powerful matrix manipulation capabilities of MATLAB to fully exploit this map type so the term matrix map is more appropriate When the data consists of surface elevations the map can also be referred to as a digital devation map DEM or topographical map 1 4 Types of Maps in the Mapping Toolbox As an example of this map type consider a 180 by 360 matrix Each row represents one degree of latitude and each column represents one degree of longitude Each entry of this matrix is the average elevation in meters for the one degree by one degree region of the Earth to which its row and column
133. he points in this format determines the direction of travel Courses are therefore calculated from each waypoint to its successor not vice versa courses distances legs waypoints courses 90 0000 70 3132 90 0000 151 8186 98 0776 131 5684 distances 145 6231 356 2117 283 6839 204 2073 854 0092 135 6415 5 30 Navigation Since this is a navigation function the courses are all in degrees and the distances arein nautical miles From these distances speeds required toarrive at Port Said at a given time can be calculated Southbound traffic is allowed to enter the canal only once per day so this information might be economically significant since unnecessarily high speeds can lead to high fuel costs Dead Reckoning When sailors first ventured out of sight of land they faced a daunting dilemma How could they find their way home if they didn t know where they were The practice of dead reckoning is an attempt to deal with this problem The term is derived from deduced reckoning Briefly dead reckoning is vector addition plotted on a chart For example if you had a fix at 30 N 10 W at 0800 and you proceeded due west for 1 hour at 10 knots and then you turned north and sailed for 3 hours at 7 knots you should be at 30 35 N 10 19 W at 1200 All s well ring eight bells on time Mr Bowditch right 30 35 N 10 19 W Q deduced position at 1200 EN Pla oO 30 N 10
134. he standard distance of geographic data is a measure of the dispersion of the data in terms of its distance from the geographic mean Among its advantages are its applicability anywhere on the globe and its single value dist stdist lat lon G eostatistics In short the standard distance is the average norm or cubic norm of the distances of the data points in a great circle sense from the mean position It is probably a superior measure to the two deviations returned by st dm except when a particularly latitude or longitude dependent feature is under examination x Am T T x 7 N Standard Distance N l x l l Mean Position xX o x ia 7 Le Equal Areas in Geostatistics A common error in applying two dimensional statistics to geographic data lies in ignoring equal area treatment It is often necessary to bin up data to statistically analyze it In a Cartesian plane this is easily done by dividing the space into equal x y squares The geographic equivalent of this is to bin up the data in equal latitude longitude squares Since such squares at high latitudes cover smaller areas than their low latitude counterparts the observations in these regions are underemphasized The result can be conclusions that are biased towards the Equator 5 7 5 Mapping Applications Geographic Histograms The geographic histogram command hi str allows you to display binned up geogr
135. hem on a Mercator projection axesm MapProjection mercator Frame on MapLatLimit 2 8 3 3 MapLonLimt 55 8 56 3 plotm lata latb latc lona lonb lonc LineStyle none Marker pentagram MarkerEdgeColor b MarkerFaceColor b Marker Size 12 5 21 5 Mapping Applications Here s what it looks like the labeling and imaginary coastlines are added after the fact for illustration Point C 3 15 N 55 95 W Point A 3 1 N 56 2 W Point B 2 95 N 55 9 W Take three visual bearings Point A bears 289 Point B bears 135 and Point C bears 026 5 Calculate the intersections newl at newl ong navfix lata latb latc lona lonb lonc 289 135 26 5 1 1 1 newlat 3 0214 Na 3 0340 Na 3 0499 Na newlong 55 9715 aN 56 0079 aN 56 0000 aN 5 22 Navigation Add the bearing lines and intersection points to the map plotm newlat newlong LineStyle none Marker diamond MarkerEdgeColor r MarkerFaceColor r MarkerSize 9 Point A a Point B Notice that each pair of objects results in only one intersection since all are lines of bearing What if instead you had ranges from the three points A B and C of 13nm 9nm and 7 5nm respectively newl at newl ong navfix lata latb latc lona lonb lonc 13 9 7 5 0 0 0 newlat 3 0739 2 9434 3 2413 3 0329 3 0443 3 0880 newl ong 55 984
136. hematically the projection is often only partially geometric Constant scale A linear scale that remains the same along a particular line on a map although that scale may not be the same as the stated or nominal scale of the map Contour All points that are at the same elevation above or below a specified datum Conventional aspect See Normal aspect Correct scale A linear scale having exactly the same value as the stated or nominal scale of the map or a scale factor of 1 0 Also called true scale G lossary Cylindrical projection A projection resulting from the conceptual projection of the Earth onto a tangent or secant cylinder which is then cut lengthwise and laid flat When the axis of the cylinder coincides with the axis of the Earth the meridians are straight parallel and equidistant while the parallels of latitude are straight parallel and perpendicular to the meridians Mathematically the projection is often only partially geometric Dead reckoning From deduced reckoning the estimation of geographic position based on course speed and time DEM Digital Elevation Map Model Elevation data in the form of a matrix map generally on a regular grid DEM also refers to the five primary types of digital elevation models produced by the U S Geological Survey one of which is the 1 degree 3 arc second resolution model that is interfaced through the Mapping Toolbox Departure The arc length distan
137. hic I nformation System A system usually computer based for theinput storage retrieval analysis and display of interpreted geographic data A 6 G lossary Globular projection Generally a nonazimuthal projection developed before 1700 on which a hemisphere is enclosed in a circleand meridians and parallels are simple curves or straight lines Graticule A network of lines representing a selection of the Earth s parallels and meridians for the purpose of projection The vertices of the graticule grid are precisely projected and the map data contained in any grid cell is warped to fit the resulting quadralateral A finer graticule grid results in a higher projection fidelity at the expense of greater computational requirements Great circle Any circleon the surface of a sphere especially when the sphere represents the Earth formed by the intersection of the surface with a plane passing through the center of the sphere It is the shortest path between any two points along the circle and therefore important for navigation All meridians and the Equator are great circles on the Earth taken as a sphere Grid See Map grid HMS Hours minutes seconds time notation of the form hh mm ss In the Mapping Toolbox when hms times are represented by a single number the format is hhmm ss Homalographic homolographic projection S E qual area projection Hydrography Thescience of measurement description and mappi
138. hic Interpolation 0 000 eee ees 1 30 PIVOT ATER 2 sa nib eee ial wee PE Rh hee 1 32 Vector Calculations Intersections 20000 1 34 Trimming Vector Data toa Defined Region 1 36 Simplifying Vector Data 0 2 0 cece ee 1 38 Working with Matrix Maps 5 1 42 Regular Matrix MapS 0 000 c cece ee ee 1 42 TheMapLegend 0 0c eee ees 1 43 The Geographic Meaning 0 0 cece eee eee 1 44 Accessing Matrix Map Elements 005 1 47 Valued Maps and Indexed Maps 0000eeaee 1 49 Matrix Maps as Logical Variables 1 51 General Matrix Maps 0 00 e cee eee 1 53 TheMap Format a enean aen mae i hae e 1 53 Geographic Interpretations 0 0 0 cee eee eee 1 56 Displaying Maps 2 Introduction to Mapping Graphics 2 2 Map Axes is cage deo G ede ye Shade ha cee Shade dewaenemeas 2 3 Accessing and Manipulating Map Axes Properties 2 6 The Map Frame 0 cece eee eens 2 11 The Map Grid 00 0 eens 2 15 Map and Frame Limits 000005 2 18 Switching Between Projections 2 19 Projected and Unprojected Objects 2 22 Displaying Vector Maps as Lines 2 24 Displaying Vector Maps as Patches 2 27 Display
139. hoose OK J apan will changetothenew color Next change the color of all other countries to a light beige by selecting4 from the Codes menu and custom fromthe Color menu Usethe Custom Color GUI to choose a light beige color then press OK Finally to change the color of water toa light blue select 3 from the Codes menu and c us t o m from the Color menu Choose a light blue from the Custom Color GUI and press OK The map of J apan now appears T SS Figure No 1 Color Map See Latitude 35 130 15 4 145 Longitude Load Select Codes _ Color _custorn_ Save 6 41 6 G UI Tools Press the Save button then press OK to accept the default namec r map for the new colormap variable The Color Map dialog box can now be closed To display the map of J apan type axes m In the Projection Control box choose a Miller Cylindrical projection and define the map latitude and longitude limits to be 24 48 and 123 149 respectively Use the Grid button to turn the grid on then press the Parallel and Meridian Settings button and set the longitude locations and latitude locations to 5 to display grid lines every 5 degrees Use the Label button to turn the meridian and parallel labels on Change the label format to none Press Parallel and Meridian Settings button and change the longitude and latitude label locations to 5 to display labels every five degrees Press Apply to apply the settings
140. ider two more variables at border and onbor der which correspond to points along the Anglo Scottish border proceeding from the west coast at Solway Firth to the east coast at Berwick upon T weed This data can really only be plotted as a line The two pairs of variables together can form a map They can be displayed as a patch of Great Britain with a line showing the border However you still would not havea polygon for matted map of Scotland alone Sf Border Line Polygon of Great Britain Combined Map 1 26 W orking with Vector M aps Creating Vector Data In addition to the vector map data available in the Mapping Toolbox and from external sources for such things as coastlines political boundaries and other more permanent objects you may want to create your own vector data for such things as great circles rhumb lines and small circles Calculating Small Circles You can calculate vector data for points along a small circle in two ways If you have a center point and a known radius usesci rcl e1 if you havea center point and a single point along the circumference of the small circle use scircle2 For example to get data points describing the small circle at 10 distance from 67 N 135 W use the following latc lonc scirclel 67 135 10 Toget thesmall circle centered at the same point that passes through the point 55 N 135 W usescircle2 latc lonc scircle2 67 135 55 135 scirc
141. ield You may find it convenient to write a small function to trade the tags without overwriting function struc switchfields struc fromfield tofield for i l length struc eval temp struc i tofield eval struc i tofield struc i fromfield eval struc i fromfield temp end for Here is a new map of the data plotted with the summer colormap 72 W 71W 70 W 69 W 44 43 42 V MARTHAS Rhode Isl a ode Island Soend NANTUCKET ISLAND BLOCK ISLAND 41 7 10 Global Vector Data The DCW does not contain all topology levels in each theme Roads for example have no patches If data is requested for topology levels that are not available the function issues a warning and returns an empty matrix Hereis a display of the road line data for the Cape Cod map RDpatch RDI ine RDpoint RDtext dcwdata cdrom NOAMER 41 44 72 69 RD all cl ma hPOline displaym POli ne hidem handlem None set hPOline Color 1 1 1 0 75 LineWi dth 1 hRDIine displaym RDline 42 7 11 7 External Data Interface The roads patterns are clearly related to settlement patterns The network of roads around Boston gives away its location The DCW alsoincludes a populated places theme containing the boundaries of built up areas Extract the PP theme reduce the displayed area to Boston and Cape Cod and plot the populated places
142. igator selects appropriate waypoints and plots them 5 28 Navigation Todothis with the Mapping Toolbox you can display a map axes with a Mercator projection select appropriate map latitude and longitude limits to isolate the area of interest plot coastline data and interactively mouse select the waypoints with thei nput m command Thet rack command will generate points to connect these waypoints which can then be displayed with pl otm For illustration assume that the waypoints are known or were gathered using input m See the Mapping Toolbox Reference Guideor Interacting with Displayed Maps to learn about usingi nput m Waypoints 36 5 36 2 38 5 38 11 35 13 33 30 31 5 32 Waypoints 36 0000 5 0000 36 0000 2 0000 38 0000 5 0000 38 0000 11 0000 35 0000 13 0000 33 0000 30 0000 31 5000 32 0000 load coast axesm MapProjection mercator MapLatLimit 30 47 MapLonLimit 10 37 framem plotm at long lttrk lntrk track waypoints plotmlttrk ntrk r 5 29 5 Mapping Applications Although these track segments are straight lines on the Mercator projection they will be curves on others The segments of a track like this are called legs Each of these legs can be described in terms of course and distance The function egs will take the waypoints in navigational track format and return the courses and distances required for each leg Remember the order of t
143. iloting Positions are fixed by correlating the bearings and or ranges of landmarks In real life piloting all sighting bearings are treated as rhumb lines while in fact they are actually great circles Over the distances involved with visual sightings up to 20 or 30 nautical miles this assumption causes no measurable error and it provides the significant advantage of allowing the navigator to plot all bearings as straight lines on a Mercator projection The Mercator was designed exactly for this purpose Range circles which might be determined with a radar are assumed to plot as true circles on a Mercator chart This allows the navigator to manually draw the range arc with a compass 5 13 5 Mapping Applications 5 14 These assumptions also lead to computationally efficient methods for fixing positions with a computer The Mapping Toolbox includes thenavf i x function which mimics the manual plotting and fixing process using these assumptions To obtain a good navigational fix your relationship to at least three known points is considered necessary A questionable or poor fix can be obtained with two known points Some Possible Situations In this imaginary coastal region you take a visual bearing on the radio tower of 270 At the sametime Gilligan s Lighthouse bears 0 If you plot a 90 270 line through the radio tower and a 0 180 line through the lighthouse on your Mercator chart the point at which the lin
144. imes if they do not occur at course changes 5 33 5 Mapping Applications Imagine you havea fix at midnight at the point 10 N 0 waypoints 1 10 0 fixtime 0 You intend to travel east and alter course at the point 10 N 0 13 E and head for the point 10 1 N 0 18 E On the first leg you will travel at 5 knots and on the second leg you will speed up to 7 knots waypoints 2 10 13 waypoints 3 10 1 18 speeds 5 7 To determine the DR points and times for this plan usedreckon drlat drlon drtime dreckon waypoints fixtime speeds drlat drlon drtime ans 10 0000 0 0846 1 0000 Position at 1 am 10 0000 0 1301 1 5373 Time of course change 10 0484 0 1543 2 0000 Position at 2 am 10 1001 0 1801 2 4934 Time at final waypoint Here is an illustration of this track and its DR points Time at 10 1 N 0 18 E is 2 4934 q Position at time 2 0 10 048 N 0 154 E Fix at midnight 10 N 0 at time 0 0 given c 090 s 5 5 Time of turn at iti 10 N 0 13 E Position at time 1 0 10 N 0 085 E is 1 5373 5 34 Navigation However you would like to get tothe final point a little earlier to make a rendezvous Y ou decide to recalculate your DRs based on speeding up to 7 knots a little earlier than planned The first calculation tells you that you were going to increase speed at the turn which would occur at a tim
145. imit 15 75 MapLonLimit 175 60 MLineLocation 15 MLabelParallel south Meri dianLabel on ParallelLabel on GLineStyle GColor 0 5 1 1 1 Grid on Frame on displaym state geoid almanac earth geoid tags state tag for i l length state lat state i lat long state i long Surfarea Sum areaint lat long geoid set handlemtags i CData surfarea end caxis 0 1 5E6 colormap hsv 15 colorbar 2 52 Specialized Map Displays The coloring scheme of the map makes it easy to distinguish which states are comparable in area The color scale to the right of the map shows the surface areas in square kilometers x 10 15 0 The largest state is Alaska about 1 5 million square kilometers while Rhode Island stands as the smallest state about 2500 square km The District of Columbia of course is the smallest entity of the dataset at roughly 200 square km 2 53 2 Displaying Maps 2 54 Atlas Data Types of Data 0 ee 3 2 World Vector Data 0 0 00 c ccc eee 3 3 Coastlines saa ios a aiaa anaia a aiat Ea aen d E A al ESR a EDI a A at Enana 3 3 World Atlas Data aaae 3 5 World Matrix Data 0 0 00 c ccc ee 3 14 Political eee eens 3 14 MEFA es aaa e ai os cans Sei ts geat ete air Ge ins daar ei anaa 3 17 United States Vector Data 000 eee 3 18 Low Resolution D
146. ing Matrix Maps 00005 2 30 TheGraticule 2 0 2 eet 2 31 Coloring Matrix Maps 0 00 c eee eee 2 34 Data Representation 0 0 0 2 36 Image and Surface Coloring 2 cee eee eee 2 36 Surface Light Shading 00 e eee eee eee 2 37 Surface Lighted Shaded Relief 00 00 ce eee 2 39 Mapped Light Objects 0 2 e eee eee 2 40 The Geographic Data Structure 2 43 Interacting with Displayed Maps 2 47 Specialized Map Displays 00 2 50 Thematic M ap Functions 000 cece ee 2 50 Choropleth Maps 0c eee eee eee eee 2 52 vi vii Contents Atlas Data 3 Types of Data Laaa 3 2 World Vector Data 0 0 0000 3 3 Coastlines erene tes cues eee ents ees Seiten oss Gated eects Gee ae 3 3 World Atlas Data 0 00 00 ee 3 5 World Matrix Data 0 00 000 000 00 3 14 Political sa iaa use ada sia aa a ee eee eee 3 14 Terral iaria Anii ct ls nar sit an et eed adh E i Ai 3 17 United States Vector Data 0 0 0 0000 3 18 Low Resolution Data 0 0 00 c ee eee 3 18 Medium Resolution State Outlines 00 3 23 United States Matrix Data 00 0 0 0 00 0 3 26 Political copies sehen ee ws Sandee os he dasa at aa wees a Brie eee ees 3 26 Terralh eee a OE a aa a a a a 3 28 Astro
147. ion of how to calculate points along great circles and rhumb lines appears later in this document Great Circle gt shortest distance _Rhumb Line Gonstant azimuth Measuring Distance When you calculate the distance between two points with the M apping Toolbox the result will depend upon whether you want a great circle or a rhumb line distance The di stance command will return the appropriate distance between two points as an angular arc length employing the same angular units as the input latitudes and longitudes The default path type is the shorter great circle and the default angular units are degrees The previous figure shows two points at 15 S 0 and 60 N 150 E The great circle distance between them in degrees of arc is as follows distgc distance 15 0 60 150 distgc 129 9712 1 10 Geographic M easurement The rhumb line distance is greater distrh distance rh 15 0 60 150 distrh 145 0288 To determine how much longer the rhumb line path is in say kilometers you can use a distance conversion function on the difference kmdifference deg2km distrh distgc kmdifference 1 6744e 03 Several distance conversion functions are available in the toolbox supporting degrees radians kilometers statute miles and nautical miles Converting distances between angular arc length units and surface length units requires the radius of a planet or spheroid By default
148. ion points are less than 4 nautical miles apart Incidentally after 1 hour the airplane would be just north of New York s Finger Lakes Small Circles In addition torhumb lines and great circles one other geographic construction is significant in geography and the Mapping Toolbox the small circle The precise definition of a small circleis theintersection of a plane with the surface of the planet In the Mapping Toolbox this definition includes planes passing through the center of the planet so the set of all small circles includes all great circles as limiting cases This usage is not universal 1 13 I apping Fundamentals Small circles are most easily defined by distance All points 45 nm nautical miles distant from 45 N 60 E would be the description of one small circle If degrees of arc length are used as a distance measurement then a great circle is the set of all points 90 distant from a particular center point For truesmall circles the distance must be defined in a great circle sense the shortest distance between two points on the surface of a sohere However the Mapping Toolbox also allows the calculation of a pseudo small circle for which distances are measured in a rhumb line sense along lines of constant azimuth These should not be confused with true small circles Great Circle as Small Circle gt 90 from point B Sooo rm nn 5 C2
149. ions as set forth in subparagraph c 1 ii of the Rights in Technical Data and Computer Software Clause at DFARS 252 227 7013 b for any other unit or agency NOTICE Notwithstanding any other lease or license agreement that may pertain to or accompany the delivery of the computer software and accompanying documentation the rights of the Government regarding its use reproduction and disclosure are as set forth in Clause 52 227 19 c 2 of the FAR Contractor manufacturer is The MathWorks Inc 24 Prime Park Way Natick MA 01760 1500 MATLAB Simulink Handle Graphics and Real Time Workshop are registered trademarks and Stateflow and Target Language Compiler are trademarks of The MathWorks Inc Other product or brand names are trademarks or registered trademarks of their respective holders Printing History May 1997 First printing Contents Preface Acknowledgments 00 cece eee c eens ii Mapping Fundamentals 1 What Is a Map 0 0 0 ccc ccc cece eens 1 2 Types of Maps in the Mapping Toolbox 1 3 Vedo MAPS sah o atgsig alae Sak Wigan aca aw Bak Ginnie Gm KRKE ERORA 1 3 Matrix Maps siaaa are sob nd tens earch a eee ane aT 1 4 Composite MapS sasssa a 1 6 Geographic Measurement 20002 2 000 1 7 Latitude and Longitude 0 0 c eee eee 1 7 Great Circles and Rhumb Lines 00002 eee eee 1 9 Measuring Distance
150. is useful for illustrating patches load usalo who Your variables are conus gtlakelon statel at uslon greatlakes State statel on gtlakel at stateborder uslat 2 27 2 Displaying Maps The variablesus at andus on together describe three polygons separated by NaNs representing the continental United States The smaller polygons are necessary to display Long Island and Martha s Vineyard The variables gtlakelat andgt akel on describe three polygons Separated by NaNs for the Great Lakes Thevariablesstatel at andst ate on contain line segment data Separated by NaNs for the borders between states which is not formatted for patch display Conic projections make good displays of the United States socreatea map axes using an Albers E qual Area Conic projection By specifying map limits that contain the region of interest you automatically center the projection on an appropriate longitude and the frame encloses just the mapping area not the entire globe A good rule of thumb for conic projections is to set the standard parallels at one sixth of the distance from both latitude limits You can do this automatically by providing an empty matrix as the standard parallel axesm MapProjection eqaconic MapParallels MapLatLimit 23 52 MapLonLimit 130 62 When patch data is displayed layering can become important as objects above can hide objects below You can control the visibility of objects by the order of
151. istance assumes a knowledge of the underlying radius On the Earth a degree of arc length is about 60 nautical miles nauticalmiles deg2nm 1 nauticalmiles 60 0405 The Earth is the default assumption for these conversion functions Other radii may be used however nauticalmiles deg2nm 1 al manac moon radius nauticalmiles 30 3338 1 24 W orking with Vector M aps Working with Vector Maps Data Format Vector maps are usually contained in a pair of variables which represent the latitude longitude pairs for points of interest For example the following two variables can be a vector map lat 45 6 23 47 78 long 13 97 45 165 Since this is a made up example these points could mean anything Perhaps they arethe locations over which geosynchronous satellites are stationed If so you might think of them as three distinct points Perhaps they represent the starting point the mid course marker and thefinish point of an airplane race Think of them as three points connected by two line segments Or perhaps they represent the vertices of a triangle bounding a region with a propensity for unexplained phenomena in which case think of them as describing a polygon The Mapping Toolbox provides functionality for each of these interpretations For many purposes the distinction is irrelevant for others the choice of a function implies the appropriate interpretation For example the command pl otm will
152. king with M atrix Maps Of course a regular matrix map can also be considered a general matrix map All that are required are the graticule or coordinate matrices which can be produced from the regular matrix map itself using the mes hgr at function Class double double double double double load topo lat lon meshgrat topo topol egend whos Name Size Bytes lat 180x360 518400 lon 180x360 518400 topo 180x360 518400 topolegend 1x3 24 topomapl 64x3 1536 topomap2 128x3 3072 double array array array array array array 1 59 I apping Fundamentals 1 60 Displaying Maps Introduction to Mapping Graphics 2 2 Map AXGS 0 0 ete 2 3 Accessing and Manipulating Map Axes Properties 2 6 The Map Frame 000 0 eee ees 2 11 The Map Grid 0 0 0 cece ee 2 15 Map and Frame Limits 0 00005 2 18 Switching Between Projections 2 19 Projected and Unprojected Objects 2 22 Displaying Vector Maps asLines 2 24 Displaying Vector Maps as Patches 2 27 Displaying Matrix Map 00 eee eee 2 30 TTS GAEL CUN GS ies riges ai Seer Aliea peace Bom Sele OR cw goaa 2 31 Coloring Matrix Maps 2 0 0 cee eee 2 34 Data Representation 0 0 0 cece ees 2 36 Mapped Light Objects 0 0 ees 2 40 The Geographic Data Structure
153. lar matrix map at the same resolution 180 by 360 as thet opo data but in this case it is an indexed map of political entities as opposed to a matrix of elevations and bathymetric data Thenat ions structure relates the indices in the map to the names of countries and the variable clrmap iS acolormap that provides a good political display of the world Display the political regular matrix map using the mes hm function and the provided colormap axesm gortho meshm map mapl egend col ormap clrmap W orld M atrix Data The map is shown in a Gall Orthographic projection more recently made familiar as the Peters projection This projection is equal area a property that is often desirable in representing competing political units The low resolution of this data makes it suitable only for global displays Larger scale regional maps are better made with vector data such as that in thewor l dl o database M ore detailed political matrix maps can be created from vector data using the techniques described in Chapter 6 of this document GUI Tools This dataset can also be used to determine which country contains a point known by its latitude and longitude What country claims sovereignty over the point at 5 E and 13 N code tln2val map mapl egend 5 13 code 34 nations code ans name Cameroon 3 15 3 Atlas Data 3 16 Work through this example to see how the result was obtained The matrix m
154. le1 scircle2 ge a perimeter point 1 N 1 a radius 5 4 I I I L I e L 1 I I center point 1 1 center point 1 N N 7 output points 1 27 I apping Fundamentals 1 28 Thescircle1 function alsoallows points along a specific arc of the small circle to be calculated For example if you want to know the points 10 in distance and between 30 and 120 in azimuth from 67 N 135 W simply provide arc limits latc lonc scirclel 67 154 10 30 120 scircle1 with arc limits 30 azimuth 1 These nr points center point are not f Mr Po are returne returned 1 1 lt 120 azimuth When an entire small circle is calculated the data is in polygon format F or all calculated small circles 100 points are returned unless otherwise specified You can calculate several small circles at once by providing vector inputs See the reference pages onscirclel andscircle2 in the Mapping Toolbox Reference Guide for more information Calculating Tracks Great Circles and Rhumb Lines You can generate vector data corresponding to points along great circle or rhumb line tracks usingt rack1 andtrack2 If you havea point on the track and an azimuth at that point uset rack1 If you have two points on the track usetrack2 For example to get the great circle path starting at 31 S 90 E with an azimuth of 45 with a length of 12 uset rack1 latgc longc trackl gc 31 90
155. lindrical 4 4 defined 2 3 4 2 defining for a map axes 2 3 distortion 4 3 equal area 4 3 equidistant 4 3 gnomonic 4 6 orthographic 4 6 polyconic 4 5 stereographic 4 6 switching 2 23 table of properties 4 22 ma pmt x workspace 1 53 mapped object versus standard object 2 22 mapped objects changing stacking order 6 28 editing properties 6 9 manipulating by name 2 48 maps 2 3 maptool 6 2 activating 6 3 6 5 calculating surface distance 6 16 Index default map projection 6 4 displaying map grid and frame 6 30 entering workspace commands 6 12 hiding mouse tool buttons 6 29 hiding objects 6 20 menus 6 4 mouse tool buttons 6 4 6 29 plotting line objects 6 13 6 24 plotting patches 6 27 plotting text objects 6 14 6 24 plotting tracks 6 16 setting map projection 6 5 6 22 setting map properties 6 5 6 22 zoom feature 6 11 maptrim 6 31 maptriml 1 36 maptrimp 1 36 maskm 1 48 mat 2dms 1 21 mat 2hms 1 23 matrix maps coloring 2 34 6 41 defined 1 4 displaying 2 30 graticules 2 31 indexed maps 1 50 6 33 6 41 logical maps 1 51 replacing entries 1 48 6 33 See also general matrix maps See also regular matrix maps valued maps 1 49 mean of geographic data 5 3 meanm 5 4 Mercator projection 4 13 5 13 5 28 meridians controlling display 2 15 defined 1 8 meshgrat 1 59 2 36 meshl sr m 2 39 2 42 mes hm 6 42 mi naxi s 1 18 ml ayers 2 48 6 7 6 27 mobj ects 6 9 mouse interaction with dis
156. lipsoid along a line that is a parallel of latitude if the plane is at right angles to the axis Shaded Relief Shading added to a map or image that makes it appear to have three dimensional aspects This type of enhancement is commonly done to satellite images and thematic maps utilizing digital topographic data to provide the appearance of terrain relief Similar projection Subjective and qualitative term indicating a moderate or strong resemblance Singular points Certain points on most but not all conformal projections at which conformality fails such as the poles on the normal aspect of the Mercator projection Skew oblique aspect An aspect of a projection on which the axis of the Earth is rotated soit is neither aligned with nor perpendicular to the conceptual axis of the map projection and tilted so the poles areat an angleto the conceptual axis of the map projection Small circle A circle on the surface of a sphere formed by the intersection with a plane Parallels of latitude are small circles on the Earth taken as a sphere In the Mapping Toolbox great circles including the E quator and all meridians are treated as special limiting cases of small circles Small scale mapping Mapping at a scale smaller than about 1 1 000 000 although the limiting scale sometimes has been made as large as 1 250 000 Spheroid See Ellipsoid Standard parallel n the normal aspect of a projection a parallel of latitude al
157. litary Specifications and Standards 7 13 7 External Data Interface U S Vector Data One of the best sources of public vector data for the United States is the U S Census Bureau This organization has developed a digital database and system for automated mapping in support of the United States decennial census The Topographically Integrated Geographic Encoding and Referencing TIGER system is used within the Bureau to carry out and analyze the census TIGER contains hydrographic features roads railroads and other transportation features scanned from 1 100 000 U S Geological Survey USGS topographic maps The database also contains census tracts and political boundaries for states counties and indian reservations it does not include topography The Census Bureau periodically publishes extracts from the TIGER database for public use in the form of TIGER Line and TIGER thinned boundary files The Mapping Toolbox provides interfaces to both formats TIGER Line TIGER Line files are extracts from the U S Census Bureau s TIGER map database Each set of files covers one municipal district and contains transportation features such as roads and railroads cultural features hydrographic features and political boundaries The data is distributed on CD ROMs by the Census Bureau TIGER Line data is not copyrighted but the Bureau does charge for the production of the CDs Ordering and other information can be found from the U S Censu
158. litical Ocean boundaries PO and Populated Places PP The data is further separated into structures containing patches lines points or text In addition to containing more kinds of data than coast this dataset is also more detailed The drainage data consists of about 7 000 points while the political lines and patches each have about 30 000 points There are more than 200 political units in the political data and more than 300 major cities in populated places Because of the quantity of data complicated displays may require more than MATLAB s default memory size and may take longer to project and render Displays of patches require the greatest memory and computing time The contents of the structures can be displayed from the command line using di spl aym For example type the following axesm mollweid framem gridm displ aym POI ine displ aym PPpoi nt 3 Atlas Data 3 6 Here is the result The map displays the coastlines international borders and major cities of the world We could also label the cities with data from the PPt ext structure but at this scale the result would be unreadable When we restrict ourselves to a smaller geographic region more information can be shown figure axesm Mapprojection eqaconic MapParallels MapLatLimit 30 60 MapLonLimit 15 45 MLabelLocation 15 MLineLocation 15 PLabelLocation 15 PLineLocation 15 GColor 5 1 1 1 GLineStyle
159. lot the flight from Hamburg to Washington D C The map now displays your flight routes SSS Figure No 1 EM Press Close to close the Define Tracks dialog box Now you are wondering which trip will cover more distance your flights from Washington D C to London to Barcelona or your return flights from Venice to Hamburg to Washington D C The answer can be easily determined using thesurfdist GUI tool Select Display Surface Distances from the menu bar The Surface Distances dialog box appears Select Great Circle 2 Point mode Thetracks are already plotted so leave the Show Track box unchecked If the Show Track box were checked the tracks would be displayed as the distances are calculated but the tracks would be deleted when the Surface Distances tool is closed To calculate the distance of your first trip you need to add the distance from Washington D C to London and the distance from London to Barcelona First enter starting point 39 17 76 86 and ending point 51 59 0 04 in the appropriate edit boxes You want your answer in miles so you need to change the range units The Complete GUI Environment maptool Press the Range Units button and the Define Range Units dialog box appears Define Range Units Normalizing Geoid km almanac earth radius Select Miles from the pull down menu and press Apply Press Compute t
160. lternate tags are availablein both abbreviated and expanded forms 7 8 Global Vector Data The following commands plot the political and ocean features on a Mercator projection hiding the ocean patches and the tile boundary lines They also override the default colormap used for the land patches and remove the edge color to hide the tile join axesm MapProjection mercator MapLatLimit 41 44 MapLonLimit 72 69 MLabel Location 1 MLineLocation 1 PLabel Location 1 PLineLocation 1 framem gridm mlabel plabel hPOpatch displaym POpatch hPOline displaym POli ne hPOpoint displaym POpoint hPOtext displaym POtext hidem handlem Open ocean hidem handlem None brown 8 5 2 set handl em Land FaceColor brown EdgeColor none set hPOtext FontSize 6 447 71 w 70 W 69 w 43 Nlassachusetts 42 8 Rhode Islan Sound ARTHAS vado ISLAND BLOCK ISLAND 41 7 9 7 External Data Interface Notice how much more detailed this map is than even the best of the atlas data provided in the Mapping Toolbox The highest resolution atlas data is in the usahi workspace which is limited to the United States The DCW covers the entire world at this level of detail The alternate tags can show the same data in a different display You can make the states different colors if you copy the alternate tags containing the state names into the primaryt ag f
161. ly useful in analyzing matrix data In the following example contour elevation lines have been drawn over a topographical map The region displayed is the Gulf of Mexico obtained from thet opo matrix Quiver plots have been added to visualize the gradient of the topographical matrix Specialized Map Displays Hereis the displayed map Hereis an example of using thes cat t er m function to create a star chart of the northern sky The stars are represented by filled circles whose size is proportional to visual magnitude Star gazers may recognize the Big Dipper constellation or Ursa Major located at 180 E 60 N 2 51 2 Displaying Maps Choropleth Maps A common type of map display has patch faces colored proportional to some specified data The data generally represents the value of something per unit area such as population density electoral votes or incidence of disease Maps of this type are generally called choropleth maps It is easy to construct choropleth maps with MATLAB and the Mapping Toolbox Simply assign the data values tothe CDat a property of the displayed patches In the following example patches representing the 50 states of the U S and the District of Columbia are displayed and colored according to the surface areas calculated by theareai nt function An equal area projection is appropriate for this kind of display load usalo axesm MapProjection eqaconic MapParallels MapLatL
162. m 2 50 R radians notation 1 21 radius of planets 1 20 raster maps Se matrix maps readfk5 7 36 reckon 1 13 reckoning position 1 13 reducem 1 38 reducing data Seevector data regular matrix maps accessing elements 1 47 defined 1 42 determining limits 1 44 determining size with scaling 1 49 displaying 2 30 6 42 image and surface coloring 2 36 shaded relief 2 39 encoding 6 33 See also matrix maps rhumb lines approximating great circle tracks with 5 28 calculating points 1 28 defined 1 9 rhxrh 1 34 rotatem 4 15 russi a workspace 1 44 Index S scatterm 2 50 5 8 scirclel 1 27 scircle2 1 27 scxsc 1 34 seconds notation 1 23 seedm 6 33 setitln 1 45 setm 2 6 2 11 2 15 setpostn 1 45 shaded relief maps 2 39 showm 2 49 simplifying data See vector data sizem 1 49 skew oblique aspect 4 12 small circles calculating points 1 27 defined 1 13 speed units format for navigation functions 5 12 spzerom 1 51 stacking order of objects changing 6 28 standard deviation of geographic data 5 5 standard parallels for conic projections 2 28 stars workspace 3 30 7 38 stdist 5 6 stdm 5 5 stem plot example 2 50 stem3m 2 50 stereographic projection 4 6 surface area accessing from almanac 1 20 measuring logical maps 1 51 polygons 1 32 quadrangles 1 15 surface distance calculating from mapt ool 6 16 measuring 1 10 surface objects displaying 2 30 surfdist 6 18 surflm 2 37 surflsrm 2 39 2 42 surf m 2 42 symbol plot e
163. m for the advertised properties The distance to Tulsa was 6 5032 distant Its colatitude in the new coordinate system is 90 83 4968 or 6 5032 Similarly the new colatitude of N ew Orleans 90 79 5273 is the distance 10 4727 Additionally the absolute difference in the azimuths of the two cities from Midland was 49 7258 The difference in their new longitudes is 48 1386 97 8644 which is also 49 7258 as advertised Matrix Data neworig A regular matrix map can be used to create a new general matrix map with its data rearranged to correspond to a new coordinate system Suppose you want to transform the topo data to a new coordinate system in which Sri Lanka 7 N 80 E is the North Pole load topo origin newpole 7 80 map at lon neworig topo topol egend ori gin 4 16 Projection Aspect Display the new map axesm miller surfm map 30 30 demcmap topo An interesting feature of this new matrix map is that every cell in its first row is 0 1 distant from the Sri Lankan point 7 N 80 E and every cell in its second row is 1 2 distant etc Another featureis that every cell in a particular column has the same great circle azimuth from the point 4 17 4 M ap Projections 4 18 Projection Computations Most of the examples in this document assume that the end product of a map projection is a graphical representation of the map While this is true for most
164. m tool To encode the map of J apan just created activate thes e edm tool by typing the following seedm map mapl egend 6 33 6 Gu Tools A new figure window displays the surface map of J apan gm Figure No 1 Seed Map a D i kd i Si os 125 130 135 140 145 Longitude Ce n of Seeds E Value L oe ga Currently your map consists of 1 s wherethereis a coastline and O s elsewhere Suppose you would like different values for four types of data coastlines 1 J apan 2 water 3 and other countries 4 Enter the values 0 and2 in the From To boxes and press Change This will change all values of 0 to 2 6 34 Constructing Personalized Map Data with G Uls To encode the regions of water enter a 1 in the of Seeds box and a 3 in the Value box Press Get and a cross hair will appear on the map Position the cross hair over a region of water and click Figure No 1 Seed Map 3 2 sar foi 130 140 145 139 Longitude ofseeds 1 vaw 3 From To 2 Press Fill In and all values corresponding to water will be changed to 3 Encode the other countries there are three regions that will need to be filled with the value 4 Encode the large region of Russia China North Korea and South K orea in the upper left of the map and the Russian I sland of Sakhalin at the top of the map in a single step
165. mapl egend 37 79 newcode 0 1 48 W orking with M atrix Maps Finally if you know the latitude and longitude limits of a region you can calculate the required matrix size and an appropriate map legend for a desired map scale Before making a large memory taxing matrix map you should first determine its size For a map of the continental United States at a scale of 10 cells per degree do the following scale 10 r c maplegend sizem 25 55 130 60 scale f 300 C 700 maplegend 10 55 130 This matrix map would be 300 by 700 What if the scale were reduced to 5 rows columns per degree scale2 5 r c maplegend sizem 25 55 130 60 scale2 r 150 C 350 maplegend 5 55 130 A 150 by 300 matrix might be more manageable Valued Maps and Indexed Maps A valued map is a matrix map in which the entries represent some value or measurement A simple example of a valued map is thet opo matrixin thet opo workspace Each entry of topo is an average elevation in meters for that piece of the Earth The entries of a valued map answer the question How much is here 1 49 I apping Fundamentals An indexed map is a matrix map in which the entries are an index value indicating where more information might be found A simple example of an indexed map is the map variable in the wor dmt x workspace Each entry of map is an index tothenati ons structure indicating which nation contains that pi
166. maplegend cells angleunit north latitude west longitude For thet opo matrix map each matrix cell represents one degree the northern edge is the North Pole and the western edge is the Prime Meridian Therefore the map legend for t opo is topolegend 1 90 0 This map legend structure is stored in thet opo workspace Imagine an extremely coarse map of the world in which each cell represents 60 Such a map matrix would be 3 by 6 and its map legend would be maplegend 1 60 90 180 0 0167 90 180 In this case the map s western edge is the International Date Line at 180 W 120 60 o 60 120 180 9 430 1 43 I apping Fundamentals 1 44 Note that the first row of the matrix is displayed as the bottom of the map while the last row is displayed as the top All regular matrix maps in the Mapping Toolbox as well as regular surfaces in MATLAB are displayed in this fashion As an example of a matrix map that does not encompass the entire world load the Cape Cod image using the oadcape script loadcape maplegend maplegend 120 44 72 Themap egend indicates that there are 120 cells per angular degree This has a horizontal resolution 120 times finer than that of thet opo matrix map which was one cell per degree Thecape region covered here extends from 41 N to 44 N and from 72 W to 69 W latlimits longlimits i mitm map map egend latlimits 41 44 longlimits 72
167. markers and labels on top of the patches by changing the stacking order Select Tools gt Objects from the menu bar The Object Sets dialog box appears Object Sets Italy h Meridian City Labels tide Delete C anta Emode hiightight Property Stacking Order Top up own etm 6 28 The Complete GUI Environment maptool Select City Markers and press Top Then select City Labels and press Top Close the Object Sets box The markers and labels are now on top of the patches Figure No 1 Your map now displays the cities you will be visiting and the track the ship will take Clicking on a country displays that country s tag in the lower left corner of the figure window Hiding the Mouse Buttons Select Tools Hide from the menu bar to hide the Zoom Rotate and Origin buttons on the figure window 6 29 6 Gu Tools Toggling the Map Grid and Frame On Tocomplete your map you want to display the grid and frame This can be done through the Projection Control dialog box or by simply selecting Display Grid and then Display Frame from the menu bar The final map looks like this Figure No 1 If you aresatisfied with your map you may want to select File gt Save from the menu bar to save the figure window in an M file When you execute the M file the figure and uicontrols will be recreated to their original a
168. method of this transformation is called a map projection from the geometric methods that were traditionally used to construct maps While many map projections no longer rely on physical projections it is useful to think of map projections in geometric terms 4 2 Quantitative Properties Quantitative Properties A sphere unlike a coneor cylinder cannot be simply reformed intoa plane In order to view the surface of a round body on a two dimensional flat plane you must first define a developable surface i e one that can be cut and flattened onto a plane without stretching and devise a means of systematically representing all or part of the spherical surface onto the plane This inevitably leads to distortions of one kind or another Three characteristic properties of map projections are subject to distortion area shape and scale A given projection cannot retain more than one of these properties over a large area of the Earth An equal area projection is onein which equal spatial units at different points on the map represent the same true area measurement For example consider a coin of any size as our spatial unit The area of the Earth covered by the coin on one part of the map display is exactly equal to that covered by the coin on any other part Shape and scale must be distorted although there are some equal area maps designed to minimize these distortions for at least parts of the map and perhaps preserve shape or
169. minate the meridians For example setting MLi neLi mit to 75 75 completely clears the polar region of displayed meridians Sometimes you might like to allow some of the meridians to ignore the limit and extend to the pole If for example MLi neException is set to 90 0 90 180 then the meridians corresponding to those four longitudes will continue past the limit on to the pole Default grid allows all displayed meridians to extend to the poles The property MLineLi mit can truncate meridians at a given latitude here at 75 N and S The property MLi neExcepti on allows certain meridians to extend to the poles despite the MLineLi mit Here four meridians 90 W 0 90 E and 180 are excepted 2 16 The Map Grid There are also corresponding map axes properties for controlling the extent of displayed parallels PLineLi mit andPLineException Users can label displayed parallels and meridians Meri di anLabel and ParallelLabel are on off properties for the display of labels on the meridians and parallels respectively They are both of f by default Initially the label locations coincide with the default displayed grid lines but you can alter this by usingthePLabel Location andMLabel Locati on properties These grid lines are labeled across the north edge of the map for meridians and along the west edge of the map for parallels However the property MLabel Parallel allows you tospecify north south equator or a
170. n Navigation Geographic Interpolation When using vector data you must be careful when you make assumptions concerning geographic reality between data points F or instance when plotting vector data you might connect each point with a straight line segment This does not usually indicate any true knowledge about the region between known points Data consisting of points along a coastline might be sparse in the absence of other knowledge filling in data can be misleading Interpreting Sparse Vector Data true coastline s interpolated points might be misleading coastline data l Despite the dangers of misinterpretation many circumstances exist in which geographic data interpolation is useful or necessary Sparser data can be linearly filled in with thei nter pm function 1 30 W orking with Vector M aps Consider a set of latitude and longitude points that you want to be no further than one degree in separation in either direction lats 12 4 5 longs 1 3 4 5 maxdiff 1 newl ats newl ongs interpm lats longs maxdi ff newlats 1 0000 1 5000 2 0000 3 0000 4 0000 5 0000 newlongs 1 0000 2 0000 3 0000 3 5000 4 0000 5 0000 In the original ats there is a gap of 2 degrees between the 2 and the 4 A linearly interpolated point 3 3 5 was therefore inserted in newl ats and newl ongs Similarly in the original ongs thereis a gap of 2 degrees between the 1 and
171. nal surface with the z coordinates given by the map matrix You can use monochrome surfaces that reflect a pseudo light source thereby producing a three dimensional shaded relief model of the surface Finally you can usea combination of color and light shading to create a lighted shaded relief map Displaying M atrix Maps The following table lists the available Mapping Toolbox surface map display functions Function Used to Create mes hm Regular matrix map warped to projected graticule mesh Sur fm General matrix map projected on map axes imagem Regular matrix map displayed as image pcolorm Projected matrix map in z 0 plane Surfacem Matrix map warped to projected graticule mesh surflm 3 D shaded surface with lighting projected on map axes meshl srm 3 D lighted shaded relief of regular matrix map surflsrm 3 D lighted shaded relief of general matrix map The Graticule The Mapping Toolbox projects surface objects in a manner very similar to the traditional methods of map making The cartographer traditionally lays out a grid of meridians and parallels called the graticule Each graticule cell is therefore a geographic quadrangle The cartographer calculates the appropriate x y locations for every vertex in the graticule grid and draws the projected graticule by connecting the dots Finally the cartographer draws the map data in freehand attempting to account for the shape of the graticule cells Similarly
172. nd correct in azimuth 3 Correct total area 4 Straight line great circles 5 Great and small circles appear as circles or lines 6 Three dimensional display 4 25 4 M ap Projections 4 26 Mapping Applications Introduction to Geostatistics and Navigation 5 2 GeostatistiCcS cc eee eee 5 3 Geographic Means 0 20 c eet te eee 5 3 Geographic Standard Deviation 002 eee 5 5 E qual Areas in GeostatisticS 00 0 c eee eee 5 7 Geographically Filtering Datasets5 11 Navigation ccee cece eee 5 12 Conventions for Navigational Functions 5 12 Fixing Position 0 00 c cece eee 5 13 PARI e MEOE E A E ET EE EEEE chain Bee ce 5 27 Track Laydown Displaying Navigational Tracks 5 28 Dead RECKONING lt cesisisci c f scp iicgions felcoam nS ach glen ole boca gage ete 5 28 TIME ZONES sick skid eee cd oh eet Pa de et aoe cade agen ade aT 5 36 Time Notation 2 0 00 cc eee 5 38 5 Mapping Applications 5 2 Introduction to Geostatistics and Navigation The Mapping Toolbox provides a set of functions for applying mapping computations to geostatistical analysis and navigation The geostatistics functions are necessary for proper analysis of geographical data as opposed to simple Cartesian x y data The navigation functions provide such useful navigational tasks as establishing position and planning routes or tracks G eostati
173. nd you want to map out your travel itinerary You will be flying out of Washington D C to Barcelona Spain with a stopover in London England At Barcelona you will board the cruise ship and sail to Monte Carlo then on to Italy sailing to Livorno Rome Naples and finally through the Straits of Messina and up the Adriatic Sea to Venice You will fly back home from Venice with a stopover in Hamburg Germany Setting Initial Map Properties First you would like to display your flight itinerary From the MATLAB command prompt type maptool This creates a new figure window and brings up the Projection Control dialog box Use the Map Projection pull down menu to initiate a Mollweide projection Projection Control Map Projection Peyl Mollweide v Angle Units Map Limits Frame Limits Latitude 90 90 Latitude 90 90 Longitude Longitude Map Origin Parallels Lat and tong o o Orientation bo Aspect Frame Grid f Labels Geoid Default Reset Apply Help cancel 6 5 6 G UI Tools Press the Grid button to activate the Map Grid Properties dialog box and turn the grid on Map Grid Properties Style Dotted ie Line Width pts Grid Altitude Li Meridian and Parallel Settings Press Accept to return to the Projection Control box and press Apply to apply the settings to the map axes E im SSS
174. nfo Interchange Format The U S Census Bureau provides thinned boundary files in the Mapl nfo Interchange Format Both U S state and county boundaries are availablein this format The Mapl nfo data files have the mif and mid extensions You will also need the _name dat file or names file containing the Federal Information Processing Standard FIPS code numbers and corresponding county names The following example reads the state boundaries of Alaska and Hawaii Five files are needed STO2 MID STO2 MIF ST15 MID ST15 MIF and st_name dat You must first read the names file for the names and FIPS codes for the U S states and territories namestruc fipsname st_name dat namestruc 1x57 struct array with fields name id 7 21 7 External Data Interface Read the file containing Hawaii s county boundaries into a geographic data structure and append it with Alaska s state boundaries STpatch tigermif namestruc ST15 MIF STpatch tigermif nmamestruc ST02 MIF STpatch STpatch 1x2 struct array with fields lat long type otherproperty tag altitude Finally to comparethe resolution and quality of this data to other sources look at the region around Cape Cod This map may look familiar to you it is the samedataintheusahi workspace plotted in a Mercator projection Theus ahi data was derived from the Census Bureau s TIGER Thinned Boundary files 72 W
175. ng of the surface waters of the Earth especially with reference to their usein navigation The term also refers to those parts of a map collectively that represent surface waters Hydrology The scientific study of the waters of the Earth especially with relation to the effects of precipitation and evaporation upon the occurrence and character of ground water Hypsography The scientific study of the Earth s topologic configuration above sea level especially the measurement and mapping of land elevation Indexed map A matrix map in which entries are an index value into another data source Thewor dmt x workspace contains an example of an indexed map Each entry in the matrix map is an index into a data structure containing the names of the world countries A 7 A Geographic Terms Indicatrix A circle or ellipse having the same shape as that of an infinitesimally small circle having differential dimensions on the Earth when it is plotted with finite dimensions on a map projection Its axes liein the directions of and are proportional tothe maximum and minimum scales at that point This is useful in illustrating the distortions of a given map projection Often called a Tissot indicatrix after the originator of the concept In the Mapping Toolbox Tissot indicatrices may be displayed using thet iss ot command and indicatrices for all supported projections are provided in the Projections Reference section of the Mapping Toolb
176. nomical Data uaaa 3 30 Map Projections 4 What Isa Projection Laa 4 2 Quantitative Properties 0 0 cece eee 4 3 Geometric SurfacesS 00 0000s 4 4 Projection Aspect 0 c cece eee eee 4 7 The Origin Vector 00 0 ce ee 4 7 Coordinate Transformations 0 000 ee eee 4 14 Vector Data rotatem saaana cee ee 4 15 Matrix Data neworig 00 e eee eee 4 16 Projection Computations 0005 4 18 Summary Guide 000 cece eee 4 22 Mapping Applications 5 Introduction to Geostatistics and Navigation 5 2 Geostatistics 0 000 nunana aaan rere 5 3 Geographic Means 0c cece eee a 5 3 Geographic Standard Deviation 0 0 eee eee 5 5 The Meaning of StdM nananana 5 5 The Meaning of stdist 2 00 c eee eee 5 6 E qual Areas in GeostatisticS 2 ccc es 5 7 Geographic Histograms 0c cece eens 5 8 Converting to an Equal Area CoordinateSystem 5 10 Geographically Filtering Datasets 000 0 ee 5 11 Navigation 0 2 c cece teen eens 5 12 Conventions for Navigational Functions 5 12 TUNES ss aaah ahd oe sect ame Shears a ae Banc a Meme baited te 5 12 Navigational Track Format 0 000 cece eee eens 5 13 Fixing Position 00 2 c cece tees 5 13 Some Possible
177. nter longitude of this zone is zd 15 ans 120 This means that at our longitude 123 E we should experience local apparent noon at 11 48 a m 12 minutes early Time Notation Navigational practice has its own peculiar notation for times Time labels on navigation plots are always in a special format Times are given in four digits hours from 00 to 23 followed by minutes from 00 to 59 So one minute before noon is 1159 or 1159Z or 1159Q etc based on time zone Similarly one minute after midnight is 0001 When more precision is required the seconds are rounded to the nearest quarter minute and zero one two or three apostrophes are suffixed to the time one for each 15 second block So 15 seconds before noon would be 1159 14 seconds before noon would have the exact same notation 5 38 Navigation The Mapping Toolbox includes the function ti me2str that returns a string in a variety of formats corresponding to a given time These strings can then be plotted on map displays as desired Two other clock formats are also allowed the 12 hour and the 24 hour digital clock readouts Consider some string notations for the time 13 21 hours after midnight The default 24 hour clock is time2str 13 21 ans 13 12 36 The 12 hour clock reads time2str 13 21 12 ans 01 12 36 PM And the navigation format for this time is time2str 13 21 nav ans 1312 Each of these can be rounded to the nearest minute
178. ntly means it includes the point defined by the Royal Observatory in Greenwich England Lines of constant longitude are called meridians Longitudes ranging from 180 to 180 are unique Longitudes may be given outside this range but such values can always be renamed to a value within therange The Mapping Toolbox provides a number of functions to convert data between different latitude and longitude ranges For example the command npi 2pi wraps data to this domain longitudes 560 125 190 newlongitudes npi2pi longitudes newlongitudes 160 0000 125 0000 170 0000 Sometimes it is more useful to consider longitude as strictly positive proceeding from the Prime Meridian 0 eastward around and back to the Prime Meridian 360 Any longitude data can be converted to this domain using thezero22pi command positivelongs zero22pi newl ongitudes positivelongs 160 0000 125 0000 190 0000 If you need this data in radians you can use an angle conversion function radianlongs deg2rad positivelongs radianlongs 2 7925 2 1817 3 3161 Several angle conversion functions are available in this toolbox supporting degrees radians and degrees minutes seconds notation 1 8 Geographic M easurement What is the antipodal point on the opposite side of the Earth of Natick Massachusetts about 42 3 N 71 35 W antilat antilong antipode 42 3 71 35 antilat 42 3000 antilong 108 6500 The result 42
179. o calculate the surface distance from Washington D C to London The answer appears next to the Rng label The distance is 3 650 7 miles from D C to London ZE Surface Distance Style Great Circle Rhumb Line Mode 1 Point 2 Point C Show Track Angles in degrees Range in miles Starting Point Lat Lon Lat 51 59 Lon 0 04 Direction Az 49 4 Rng 3650 7 Next enter starting point 51 59 0 04 and ending point 41 53 2 25 and press Compute to calculate the distance from London to Barcelona The answer is 702 9 miles The total distance covered on your trip from Washington D C to Barcelona is 3 650 7 702 9 4 353 6 miles 6 19 6 Gu Tools Similarly computing the distances from Venice to H amburg and from Hamburg to Washington D C you find your trip back home covers 583 0 3 980 5 4 563 5 miles Press Close to close the Surface Distance dialog box Hiding Mapped Objects Suppose you now want to modify the map to detail the course of the cruise ship First you want to hide the track lines city markers and city labels and leave only the coastlines displayed This can be accomplished using the mobj ects GUI as was done previously to delete the international boundaries It can also be done by selecting the Tools gt Hide Object option from the mapt ool menu bar File Edit Window Session Map Display BOWES Colormaps Hide Off Zo
180. ocation 1 Plinelocation 1 GLineStyle ml abel MLabelLocation 1 plabel PLabelLocation 1 meshm map mapl egend demcmap map 3 28 United States M atrix Data Hereis the result 43 42 Av Global coverage of digital terrain and bathymetry at this resolution is provided through the Mapping Toolbox External Data Interface A variety of freely available digital elevation maps is available over the Internet for import into MATLAB These maps range in resolution from about 10 km to 100 meters See Chapter 7 External Data Interface for more information on the data and import functions 3 29 3 Atlas Data 3 30 Astronomical Data Although the Earth may be the most commonly mapped object the same cartographic techniques are used to map the stars and planets As an example of such astronomical data the Mapping Toolbox includes a map of the stars in thestars workspace load stars whos Name Size Bytes Class gl at 4652x1 37216 double array gl ong 4652x1 37216 double array lat 4652x1 37216 double array long 4652x1 37216 double array pvmag 4652x1 37216 double array v mag 4652x1 37216 double array This is a set of more than 4500 star locations and visual magnitudes derived from the Fifth Fundamental Catalog of Stars parts and II FK5 and FK5e Other star data such as mean errors proper motions spectral types parallaxes radial velocities and cross identifications to other catalogue
181. om Tool Set Limits Full View Rotate Origin 20 View Objects Hide iq Al Delete p Map Object pa 3 6 20 The Complete GUI Environment maptool The Select Object dialog box is activated listing all currently mapped objects Select Object gt gt Parallel Select all Select Great Circle Track and press Ok The great circle tracks are then hidden Do the same for thet ext and ine objects then close the Select Object box For more information on using GUIs to edit properties of mapped objects see the GUI Reference section of the Mapping Tool box Reference Guide 6 21 6 G UI Tools Editing Map Projection and Display Properties You can display the navigational tracks of the ship by identifying waypoints and plotting them on a Mercator projection then connecting the points by using thet rack command This will result in a series of rhumb line constant direction tracks The tracks appear as straight lines on the Mercator projection but they appear curved on others Select Display gt Projection from the menu bar and change the map projection toa Mercator Cylindrical Change the map latitude limits to 36 47 the longitude limits to 5 20 and the map origin to 0 7 5 0 Always reset the appropriate map properties when switching projections or when changing map or frame limits In this case the frame limits should be reset for the new map limits Cl
182. ong which the scaleis as stated for that map There are one or two standard parallels on most cylindrical and conic map projections and oneon many polar stereographic projections Stereographic projection A specific azimuthal projection or type of projection in which the Earth is projected geometrically onto a surface from a fixed or moving point on the opposite face of the Earth A 13 A Geographic Terms Tangent cone or cylinder A cone or cylinder that just touches the sphere or ellipsoid along a single line This line is a parallel of latitude if the axes of the geometric figures coincide Thematic map A map designed to portray primarily a particular subject such as population railroads or croplands Tissot indicatrix See ndicatrix Topographic map A map that usually represents the vertical positions or elevations of features as well as their horizontal positions Thet opo workspace contains a simple example Transformed latitudes longitudes or poles Graticule of meridians and parallels on a projection after the Earth has been turned with respect to the projection so that the Earth s axis no longer coincides with the conceptual axis of the projection Used for oblique and transverse aspects of many projections Transverse aspect An aspect of a map projection on which the axis of the Earth is rotated so that it is at right angles to the conceptual axis of the map projection For azimuthal projections this a
183. ontains its southern edge and the westernmost column column 1 contains its western edge except when the map encompasses the entire 360 of longitude In that case the westernmost edge of the first column is not included because it is identical to the easternmost edge of the last column These exceptions ensure that all points on the globe can be represented exactly oncein a regular matrix map W orking with M atrix Maps Although each map matrix entry represents an area not a point it is often convenient to assign singular coordinates for reference An entry is defined by the point in the center of the area represented by the entry For example reference the center cell coordinate for the 3rd row 17th column of the Russia map row 3 col 17 lat long setIltIln map mapl egend row col lat 35 5000 long 18 3000 Since the cells in the Russia matrix map represent 0 2 squares 5 cells per degree the cell in question extends from 35 6 S to 35 4 S and from 18 2 E to 18 4 E Accessing Matrix Map Elements The actual values contained within the map matrix entries are important as well The Mapping Toolbox provides several functions for accessing and altering the values of matrix map entries If the actual row and column of a desired entry are known then a simple matrix index can return the appropriate value Use the row and column from the last example 3rd row 17th column to determine the value of that
184. or the entire tile Likewise if you request a point location the entire 5 by 5 quadrangle is returned All objects are cut at the edges of the tiles 7 External Data Interface The kind of information in an element of the structure is described by the tag field There are 8 kinds of boundary lines in this region uni que strvcat POline tag rows ans None Administrative boundary primary Definite Administrative boundary primary Poly closure line Administrative boundary primary River when boundary Coastal Closure Line None Coastline Definite Connector None International boundary Dejure Definite You can extract more than one topology level using a cell array of level names Extracting patches and points is moretime consuming sothis will take longer than the previous example The following example assumes that the NOAMER CD ROM is mounted on a Unix computer as cdrom POpatch POpoint POtext dcwdata cdrom NOAMER 41 44 72 69 PO patch point text POpatch 1 ans type patch otherproperty altitude lat 6x1 double long 6x1 double tag Land tag2 N US MAI NE tag3 North America United States MAI NE The patch and point data in this examplehaveprimary tags of Land or Open Ocean Therearealsoalternatetags containing high level political units such as nations and subordinate units such as provinces or states The a
185. origin forward degrees glon glon newcntrlon Astronomical Data The stars in galactic coordinates are commonly displayed in a pseudo cylindrical projection like the Mollweide figure axesm mol wei d framem gridm mlabel plabel setm gca MLabelLocation 120 60 180 MLineLocation 15 MLabel Parallel equator GLineWidth 01 GLineStyle FlatLimit inf 90 scatterm gl at glon pvmag MarkerSize 0125 7 41 7 External Data Interface 7 42 Geographic Terms A Geographic Terms Glossary Notes This glossary of geographical terms is drawn extensively from An Album of Map Projection U S Geological Survey Professional Pape 1453 by J ohn P Snyder and Philip M Voxland The purpose of this glossary is to assist the user in understanding the Mapping Toolbox For this reason some terms in this glossary are specifically defined as they are used in this guide rather than as they might be more generally used in the geographic community G lossary Glossary Antipodes Two points on opposite sides of a planet Arc second 1 3600th of a degree 1 second of latitude or longitude ARC Info A largely UNI X oriented GIS developed and distributed by the Environmental Systems Research Institute Inc Aspect The conceptual placement of a projection system in relation to the Earth s axis direct normal polar equatorial oblique and so on Aut
186. ot find the geoid vector you need you can create it in the following form geoidvec Semi major axis eccentricity Notethat the default units for the geoid semimajor axis in thea manac function are kilometers which can be used by simply passing in an empty matrix in place of the input units string as in the previous example Eccentricity is dimensionless Measuring the Planets The Mapping Toolbox contains a function that provides almanac data on the major bodies of our solar system Geophysical data such as geoid vectors radii surface areas and volumes can be accessed for the Sun the Earth s moon and all of the planets in any of the supported units of distance measurement Many planets have ellipsoidal geoid vectors available Some planets return spherical geoid vectors only almanac earth geoid nautical miles ans 3443 92 0 08 almanac mars geoid kilometers ans 3396 90 0 11 almanac moon geoid statutemiles ans 1079 97 0 1 19 I apping Fundamentals When a radius is desired a scalar is returned representing the radius of the best spherical model of the planet N otice that for a spherical model the radius in radians is 1 almanac mercury radius kilometers ans 2439 almanac neptune radius radians ans 1 Surface areas and volumes are calculated based on a spherical model by default In most cases you can use the geoid model instead and for the Earth y
187. ou can specify any of the supported geoid models Y ou can also request the actual tabulated values of the Earth almanac mars surfarea kilometers geoid ans 1 4441e 08 almanac earth volume kilometers international ans 1 0833e 12 almanac earth volume kilometers actual ans 1 0832e 12 A complete description of available data is provided under thea manac reference page in the Mapping Reference chapter of the Mapping Tool box Reference Guide 1 20 Angles Times and Distances Units and N otation Angles Times and Distances Units and Notation Angular Notation Angles can be represented as variables in the Mapping Toolbox in three ways degrees radians and degrees minutes seconds The toolbox provides functions for converting between these formats Degrees This is the default angular unit notation for the toolbox Although for most scientific applications radians are more commonly used in geographic usage degrees are much more convenient Degree notation is simply decimal notation in terms of degrees F orty three and one half degrees would be 43 5 Radians Radian notation is simply decimal notation in terms of radians Two radians would be 2 0 Degrees Minutes Seconds Degrees minutes seconds or dms notation is a little more complicated In text a dms angle would be ddd mm ss For example 142 15 27 is 142 degrees 15 minutes and 27 seconds The
188. ou can view the names of the objects in the current axes using na mem nhamem ans Coastline PLabel MLabel Meridian Parallel Frame Change the line width of the coastline set handlem Coastline LineWidth 2 Hide then show all of the objects of type t ext regardless of their tags hidem alltext showm all text For more information on the use of these functions and tools consult the Mapping Toolbox Reference Guide under the headings for handl em hi dem showm cl mo namem tagm andmobj ects 2 49 2 Displaying Maps Specialized Map Displays Thematic Map Functions The Mapping Toolbox provides a wide variety of other display and symbology functions Thecomet m and qui ver m functions operate like their MATLAB counterparts comet and quiver Thest em3m command allows you to display geographic bar graphs Like the MATLAB scatter command thescatterm function allows you to display a thematic map with proportionally sized symbols Thetissot function calculates and displays Tissot ndicatrices For more information on these capabilities consult the descriptions of these functions in the Mapping Reference section of the Mapping T ool box Reference Guide Hereis an example of a stem plot over a map of the continental United States The bars could represent anything from selected city populations to the number of units of a product purchased at each location Contour and quiver plots can be extreme
189. ovided ina number of useful formats in theus al o workspace load usalo whos Name Size Bytes Class conus 1x1 71072 struct array greatlakes 1x3 22220 struct array gtlakel at 1229x1 9832 double array gtlakelon 1229x1 9832 double array State 1x51 256986 Struct array stateborder 1x1 38390 struct array statelat 2345x1 18760 double array statelon 2345x1 18760 double array uslat 4339x1 34712 double array usl on 4339x1 34712 double array There are several types of data here The double arrays are vectors of latitude and longitude points The pair us at andus on form the outline of the coast and political borders of the continental United States The polygon closes on itself soit may be filled as a patch Next thestatelat andstatel on form the borders between the states for display as lines Finally gt akel at and gtl akel on are patchable outlines of the Great Lakes The commands suitable for displaying vector data of this type are pl ot m inem fillm patchm and patchesm 3 18 United States Vector Data Display the data vectors as patches and lines axesm MapProjection eqaconic MapParallels MapLatLimit 24 50 MapLonLimit 130 65 MLabel Location 15 MLineLocation 15 PLabelLocation 15 PLineLocation 15 GColor 5 1 1 1 GLineStyle MLabel parallel south framem gridm mlabel plabel patchmuslat uslon 0 75 0 patchmgtlakelat gtlakelon 1 0 0 75 plotm statelat stat
190. ox Reference Guide Interrupted projection A projection designed to reduce peripheral distortion by making use of separate sections joined at certain points or along certain lines usually the Equator in the normal aspect and split along lines that are usually meridians There is normally a central meridian for each section The M apping Toolbox does not include interrupted projections but the user can separate data into sections and project these independently to achieve this effect Large scale mapping Mapping at a scale larger than about 1 75 000 although this limit is somewhat flexible Latitude geographic The angle made by a perpendicular toa given point on the surface of a sphere or ellipsoid representing the Earth and the plane of the Equator positive if the point is north of Equator negative if it is south One of the two common geographic coordinates of a point on the Earth Latitude of opposite sign See Parallel of opposite sign Legs Line segments connecting waypoints Legend S Map legend Limiting forms The form taken by a system of projection when the parameters of the formulas defining that projection are allowed to reach limits that cause it to be identical with another separately defined projection Logical map A binary matrix map consisting entirely of 1s and Os An example of a logical matrix map can be created with thet opo map by performing a logical test for positive elevations t 0po gt 0 Each
191. p axes if its User Dat a property contains a structure defining a map projection A projection is the systematic means of representing three dimensional geographic data in twodimensions a topic that is covered more extensively in Chapter 4 Map Projections Here it is sufficient to understand that many different projections are available each with different features Some projections maintain correct relative area between objects for example or correct angular relationships Some are well suited to displaying features at certain latitudes or with certain orientations The command maps displays a list of available projections When creating a map axes object you must define its projection by using an appropriate ID string All other properties can be set by default For example the following are all valid commands for creating a Miller projection map axes axesm miller axesm miller axesm MapProjection miller Other properties can be set for the map axes during creation as well axesm MapProjection mercator Frame on AngleUnits degrees FontName courier parallellabel on Origin 0 180 0 2 Displaying Maps If you specify some map axes parameters with axes m the Mapping Toolbox determines appropriate values for other related map axes properties As an example create a map axes with an E qual Area Conic projection for part of the world axesm MapProjection eqaconic
192. phy especially for mapping regions with predominantly north south extent One candidate for such handling might be Chile Oblique Mercator projections might be used to map long regions that run neither north and south nor east and west such as New Zealand The features of a projection are maintained in any aspect relative to the base projection As we have Seen the outline or frame doesn t change Non directional features also do not change For example the Sinusoidal projection is equal area and is soin any aspect Directional features must be considered carefully however In the normal aspect of the Sinusoidal projection scale is true along every parallel and the central meridian This is not the case for the skew oblique aspect however scale is true along the lines where these parallels and meridian would be in the corresponding base projection The base projection can be thought of as a standard coordinate system and the normal aspect conforms toit The other aspects can be thought of as coordinate transformations 4 13 4 M ap Projections Coordinate Transformations Previously we discussed the concept of altering the display aspect of a map projection One way to think of this is to consider redefining the coordinate system and then displaying a projection based on the new system For example think about redefining your coordinate system so that your hometown is the origin If you calculated a map projection in a
193. played maps 2 47 selecting points with 6 26 N namem 2 49 nanm 1 51 navfix 5 12 5 19 navigation angular conventions 5 12 calculating course and distance 5 30 calculating dead reckoning positions 5 33 calculating waypoints 5 28 connecting waypoints 5 29 distance conventions 5 12 fixing position 5 13 5 19 retrieving time zone for longitude 5 36 5 38 speed conventions 5 12 navigational fixing 5 13 5 19 navigational tracks connecting waypoints 5 29 displaying 5 28 displaying from mapt ool 6 27 format 5 13 plotting from maptool 6 16 selecting waypoints with mouse 6 26 neworig 4 16 newpole 4 15 4 16 normal aspect 4 7 npi2pi 1 8 1 7 Index 1 8 0 oblique aspect 4 8 onem 1 51 orientation 4 10 orientation See origin vector origin vector 4 7 4 10 See also projection aspect orthographic projection 4 6 P parallels controlling display 2 15 defined 1 7 patch drawing functions differences between 2 29 patch objects displaying 2 27 plotting from mapt oo 6 27 patchesm 2 29 pat chm 2 29 piloting Seenavigational fixing planetary data 1 19 plot3m 2 28 plotm 2 24 polyconic projection 4 5 polygon displaying as line object 2 24 displaying as patch object 2 27 surface area 1 32 projection Seemap projection projection aspect 4 7 normal 4 7 oblique 4 8 See also origin vector skew oblique 4 12 transverse 4 8 projection control dialog box setting map projection 6 5 6 22 setting map properties 6 5 6 22 quiver
194. ppearance 6 30 Constructing Personalized Map Data with G Uls Constructing Personalized Map Data with GUIs Trimming an Existing Data Set You can use the mapt r i m tool to trim a map dataset For example you want to work with just a portion of the coastline data found in thec oast workspace say theregion around J apan Usethemapt ri m tool totrim the coastline data tothis region then save the trimmed dataset as a new vector or matrix map load coast maptrim at long A new figure window displays the unprojected coastline data Drag the zoom box to the region around J apan Figure No 1 Customize Map gt ped oa pas l 6 31 6 G UI Tools Double click in the box tozoom in Repeat this process until the area of interest fills the figure window Eo Figure No 1 Customize Map T T T T T f i Ez ae Saree ee PSPS NES Ee aa a tses a ae a EM Ly i F a0 Hh ang epelena n a ees g oe A a ay i x oN EY CEA erie ees Sr pike sihcst A A hae we Sl Ee errr tee ETS eee eee ETE ae fo 1 25 pf niveauer Tai EI ivinanvinris eens 120 130 140 150 160 Longitude Select Customize gt L imits to specify the exact limits of the region of interest A dialog box appears with the latitude and longitude limits of the current display Set the latitude limits to 24 48 and the longitude limits to 123 149 Press OK Enter the Map limits
195. projection Objects displayed using standard MATLAB commands likepl ot fill surface andtext are placed in the designated x y location If the projection changes for a map axes for example by using thes et m command to alter theMapPr oj ection property those objects displayed with standard commands are unaffected but those displayed using mapping commands are reprojected into new positions Here is an example axesm miller framem on gridm on showaxes grid off This set of commands creates a map axes a map frame enclosing the region of interest and geographic grid lines The x y axes which are normally hidden are displayed and the MATLAB x y grid is turned off It should be noted that the MATLAB x ygri d isseparatefrom the Mapping Toolbox geographic version gridm text 5 1 Standard Text Obj ect textm 60 150 Mapped Text Obj ect Here a standard text object is placed at x 0 5 and y 1 while a mapped text object has been placed at 60 N 150 W in the Miller projection 25r lt Mapped Text Object al Standard Text Object Projected and Unprojected O bjects If we change the projection to a Sinusoidal the standard text object remains at the same Cartesian position so its latitude longitude position is altered The mapped text object remains at the same geographic location so its x y position is altered Also the frame and gridlines are replaced according to the new map projection setm g
196. ptional C kgd Other Properties FontSize 8 Tag City Labels City markers and labels now appear on the map The Click and Drag Property Editor can be used to easily edit the label locations to be more pleasing to the eye Your map might then look something like this Bl SSS Figure No 1 E mmi 6 25 6 G UI Tools Selecting Track Waypoints To select track waypoints for the cruise ship use thei nput m command Select Session gt Command from the menu bar and enter the following in the Workspace Command box waylat waylon inputm Press Apply when done A cross hair appears on the map display allowing you to usethe mouse to click on the desired waypoints You know that you will be sailing from Barcelona around the islands of Mallorca and Menorca to Monte Carlo then to Livorno Rome Naples through the Straits of Messina and up the Adriatic to Venice Usethemouse to click on points that trace out such a path then press Return The Status Report box appears to let you know the operation was successful Press OK The variables way at and wayl on are now in the workspace This can be confirmed be selecting Session gt Variables from the menu bar to view the current workspace variables Creating a Navigational Track Now you can use thet rack command to connect your waypoints Select Session gt Command from the menu bar and ent
197. pty matrix for any of the property values setmgca FlatLimit MapLatLimit getm gca MapLatLimit getmgca FlatLimit ans 90 90 Inf 89 You will also need to manually specify the locations of the meridian and parallel labels setm gca MLabelParallel 0 PLabelMeridian 90 Switching Between Projections Now the map is displayed correctly with the frame Default property values can be accessed by the use of empty matrices as shown in the last example and the properties can be reset according to the new values The entire set of properties can be reset to their default values by pressing the Reset button on theaxes mui GUI For complete descriptions of all map axes properties consult the axes m reference page in the Mapping Reference section of the Mapping T ool box Reference Guide For more information on the use of axes mui refer to its reference page in the GUI Reference section of the Mapping T ool box Reference Guide or read the section of this document entitled Editing Map Projection and Display Properties located in Chapter 6 GUI Tools 2 21 2 Displaying Maps 2 22 Projected and Unprojected Objects All objects displayed using Mapping Toolbox commands are projected on the map axes based on their designated latitude longitude positions The latitudes and longitudes are mathematically transformed to x and y positions using the formulas for the current map
198. r with the Robinson projection as the default I n the upper left corner of the figure window is a set of three mouse tool buttons that allow interactive display manipulation The Menus There are five pull down menus associated with mapt oo The Session menu manipulates the workspace and sets the figure window renderer for the mapt ool session The Map menu command activates GUIs that are used to project objects onto the map axes The Display menu edits map axes properties manipulates display settings and calculates and displays navigational tracks small circles and surface distances The Tools menu provides a variety of miscellaneous mapping tools The Colormaps menu allows for manipulation of the colormap for the current figure The Mouse Tool Buttons There are three mouse tool buttons associated with mapt oo e The Zoom button toggles Zoom mode on and off Zoom mode zooms in on a two dimensional map display e The Rotate button toggles Rotate 3 D mode on and off Rotate 3 D interactively rotates the view of a three dimensional plot e The Origin button toggles Origin mode on and off Origin mode interactively modifies the map origin For more details on the mapt 00 menus and buttons see the GUI Reference section of the Mapping Toolbox Reference Guide The Complete GUI Environment maptool Activating GUIs with maptool A Working Example Suppose you are planning a cruise this summer a
199. r azimuthal projections and frame or map limits MapLat Li mi t and MapLonLi mi t map axes properties for non azimuthal projections The trimming is done internally in the display routine sothe original data remains intact See Map Axes in Chapter 2 of this document along with the reference pages for the trimming functions in the Map Reference section of the Mapping Toolbox Reference Guide for further information on trimming geographic vector data 1 36 W orking with Vector M aps Load thecoast MAT File and trim the vector data to a region centered on Australia load coast whos Name lat long latlim 50 0 Size 9589x1 9589x1 longlim Bytes 76712 76712 Class double array double array 105 160 linelat inelong maptrim lat long atlim onglim polylat pol ylong maptrimp lat long latlim longlim whos Name lat latli line line long longl i poly poly Size 9589x1 1x2 870x1 870x1 9589x1 1x2 1020x1 1020x1 Bytes 76712 16 6960 6960 76712 16 8160 8160 Class double array double array double array double array double array double array double array double array 1 37 I apping Fundamentals Simplifying Vector Data Sometimes you may need to reduce the number of points in your vector data while still maintaining an accurate representation of the geographical data A quick and easy method would be to throw out ever
200. re are 60 seconds in a minute and 60 minutes in a degree In the Mapping Toolbox when dms angles are represented by a single number the format is dddmm ss F or example 142 15 27 is 14215 27 The real value of this notation is for the input of data already in this format The toolbox includes the mat 2dms function for easily entering dms data A special case of the dms format is the dm format in which seconds are not included 1 21 10 apping Fundamentals If you havea three column matrix in which the columns are degrees minutes and seconds respectively mat 2dms will convert it to dms format dmsmatrix 45 13 46 156 45 01 7 34 12 1 dmsmatrix 45 0000 13 0000 46 0000 156 0000 45 0000 1 0000 7 0000 34 0000 12 1000 dmsformat mat2dms dmsmatri x dms format 1 0e 04 0 4513 1 5645 0 0734 NOTE Care must be exercised when working with the dms format for example two angles in this format cannot simply be added It is advisable to convert dms data to decimal degrees before working extensively with it Converting Between Angle Unit Formats The toolbox includes a variety of angle unit conversion functions F or example to convert the dms format values to degrees or to radians you can use dms2deg and dms2rad respectively degformat dms2deg dmsformat degformat 45 2294 156 7503 7 5700 radformat dms2rad dmsformat radformat 0 7894
201. reat Lakes Importing DCW Themes Although the gazette feature of the DCW is extensive the DCW is designed primarily as a database of geographic information for more general mapping applications Thedcwdat a function is used to access the map data The volume of data on the DCW is solarge that you must limit your requests toareasonable amount First select the geographical area of interest by giving the name of one of the libraries in the DCW Thereis one CD for each library NOAMER North America EURNASIA Europe and Northern Asia SOAMAFR South America and Africa and SASAUS Southern Asia and Australia You may also need to specify the device name of the CD just as you did for the dcwgaz function The geographic region of interest is further restricted providing latitude and longitude limits in units of degrees You also need to specify which theme or type of data you wish to extract Themes are layers of data related to a kind of feature like roads and drainage and are listed by two letter strings If you enter a code that isn t recognized a list of valid codes and their descriptions will be displayed 7 External Data Interface Finally you need to indicate what type of graphic objects you want patches lines points or text These are called topology levels If the NOAMER CD is available you can see the list of available themes by entering an incorrect one like The
202. ret this graphically remember that the logical matrix map topo gt 0 is binary The following is a display of the map with black where the condition is true i e the logical map entry is 1 and white where it is false 0 It is displayed in an Equal Area Cylindrical projection which vertically shrinks rows near the poles to show their true relative area Similarly thear ea mat command shrinks the contribution of these rows to the total area 1 52 W orking with M atrix Maps General Matrix Maps In addition to regular matrix maps the Mapping Toolbox provides another matrix map format general matrix maps These maps can be displayed and their values and coordinates can be queried but much of the functionality available for regular matrix maps cannot be exploited for general matrix maps The examples thus far have shown maps that covered simple regular quadrangles that is geographically rectangular General matrix maps in addition to these rectangular orientations can have other shapes as well The Map Format Todefinea general matrix map you need three variables the matrix of indices or values associated with the mapped region a matrix giving cell by cell latitude coordinates and a matrix giving cell by cell longitude coordinates An example of an irregularly shaped general matrix map is available in the Mapping Toolbox for examination load mapmt x whos Name Size Bytes Class lgl 50x50 2000
203. rmat geographic areas can be calculated using the command ar eai nt The function performs a numerical integration using Green s Theorem for the area on a surface enclosed by a polygon Since this is a discreteintegration on discrete data the results are not exact Nevertheless the method provides the best means of calculating the area of arbitrarily shaped regions Better measures result from better data 1 32 W orking with Vector M aps The Mapping Toolbox function areai nt for area by integration like the other area functions ar eaquad andar eamat returns areas as a fraction of the entire planet s surface unless a radius is provided Here we calculate the area of the continental United States using theus al o workspace Three areas are returned because the data contains three polygons Long Island Martha s Vineyard and the rest of the continental U S load usalo earthradius almanac earth radius area areaint uslat uslon earthradius area 1 0e 06 7 9256 0 0035 0 0004 Since the default Earth radius is in kilometers the area is in square kilometers From the same workspace the areas of the Great Lakes can be calculated this time in square miles earthradius almanac earth radius miles area areaint gtlakelat gtlakelon earthradi us area 1 0e 04 8 0124 1 0382 0 7635 Again three areas are returned the largest for the polygon representing Superior Michigan and Huron tog
204. rojection often a straight line about which the projection is symmetrical A Geographic Terms Central projection A projection in which the Earth is projected geometrically from the center of the Earth onto a plane or other surface The Gnomonic and Central Cylindrical projections are examples Choropleth A map consisting of areas of equal value separated by abrupt boundaries and colored or shaded according to those values Complex curves Curves that are not elementary forms such as circles ellipses hyperbolas parabolas and sine curves Composite projection A projection formed by connecting two or more projections along common lines such as parallels of latitude necessary adjustments being made to achieve fit The Goode H omolosine projection is an example Conformal projection A projection on which all angles at each point are preserved Also called an orthomorphic projection Conceptually projected The convenient way to visualize a projection system although it may not correspond to the actual mathematical projection method Conic projection A projection resulting from the conceptual projection of the Earth onto a tangent or secant cone which is then cut lengthwise and laid flat When the axis of the cone coincides with the polar axis of the Earth all meridians are straight equidistant radii of concentric circular arcs representing the parallels but the meridians are spaced at less than their true angles Mat
205. rsection of the tracks is at 37 N 41 7 W which is roughly 600 nautical miles west of the Azores in the Atlantic Ocean Y M Y 37 07 N 41 72W Norlok Dakar 1 35 I apping Fundamentals Trimming Vector Data to a Defined Region Sometimes vector data may extend beyond the geographic region of interest For example if you have world coastline data but you require a map of Australia only you may want to create new variables that contain only the data you need You might also want to trim your data to save memory or to speed up calculations and display We can distinguish between trimming line data and patch data Line data can be trimmed by simply removing points outside the region of interest Patch data requires a more complicated method to ensure that the patch objects are correctly displayed For the vector data two functions are available to achieve this If the variables are to be treated as line data the mapt ri ml command will return variables containing only those points in the defined region If polygon format must be retained the mapt ri mp command will ensure this although compared totheline formatted data the patch trimmed data will be larger and take more time to compute It should be noted that for viewing purposes trimming the data before display is not required The vector data is automatically trimmed to the region specified by the frame limits FLat Li mit and FLonLi mit map axes properties fo
206. rted back to Greenwich coordinates using theeqa2grn command lat lon ega2grn x y Remember when converting back and forth between systems latitude corresponds to y and longitude corresponds to x 5 10 G eostatistics Geographically Filtering Datasets Often a set of data will contain unwanted data mixed in with the desired values For example your data might include points for the entire United States but you only want to work with those points falling in Alabama or perhaps the dataset is untidy out of 4 000 points you notice that 3 or 4 obviously fall outside of reality for example one of your city points is in the middle of the ocean It can be quite a chore to look at each dataset element individually Perhaps selecting a portion of the data is part of your analysis Thef i ter m command works with a matrix map tofilter a vector dataset The form is of the following flats flons filterm lats ons map map egend all owed In short each location defined by ats and ons is compared to the value at that point in map If the valueis al owed that point is included inf ats and flons The map might be a politically indexed map and the allowed values might be the code or codes corresponding to the states or countries desired e g Alabama The map might also be a valued map or a logical condition thereon and theallowed value might be 1 for true Here s what an example might look like using th
207. rther on Martha s Vineyards by providing appropriate latitude and longitude limits for theusgsdem function at full resolution You can see some terracing effects in the data which correspond to its derivation from topographic contour maps map maplegend usgsdem providence e 1 41 2946 41 4829 70 8429 70 4379 axesm mercator meshm map mapl egend size map map demcmap map lightm41 4 70 65 material 7 7 1 5 lighting gouraud 7 35 7 External Data Interface 7 36 Astronomical Data The Mapping Toolbox provides an interface to a set of astronomical data called FK5 the Fifth Fundamental Catalog of Stars This catalog consists of positions proper motions and other characteristics for over 4500 stars The data is provided by the Astronomical Data Center ADC located at the NASA Goddard Space Flight Center and can be retrieved over the Internet at the ADC s home page at http adc gsfc nasa gov or by anonymous FTP at ftp adc gsfc nasa gov Documentation and other information can be found at these sites as well The data comes in two files F K5 dat and fk5_ext dat You can read both files using ther eadf k5 interface function There are more than four thousand stars in the catalog so reading and processing the data takes a while fk5 readfk5 FK5 dat fk5e readfk5 fk5_ext dat whos Name Size Bytes Class fk5 1x1535 5042752 struct array fk5e 1x3117 10226424
208. rties can be manipulated The frame is actually a patch with a default face color set to none anda default edge color of black These map axes properties can be altered by manipulating theFFaceCol or andFEdgeCol or properties For example the command setm gca FFaceColor cyan can make the background region of your display resemble water Since the frame patch is always the lowest layer of a map display other patches perhaps representing land will appear above the water If an object is subsequently plotted below the frame patch the frame altitude can be recalculated tolie below this object with the command f ramem reset The frameis replaced and not reprojected The line width of the edge which is 2 points by default can be set using the FLi neWi dth property The primary advantage of displaying the map frame is that it can provide positional context for other displayed map objects For example when vector data of the coasts is displayed the frame provides the edge of the world In addition to establishing frame properties upon map axes creation or through thes et m command you can use the f r ame m command The command f ramem aloneis a toggle for theFr ame property which controls the visibility of the frame You can also call f r amem with property names and values to alter the appearance of the frame framem FlineWidth 4 FEdgeColor red The Map Grid The Map Grid In The Mapping Toolbox
209. s SR railroads RR hydrography H area landmarks AL and point landmarks PL This isa subset of the total available data in the TIGER Line files which contain more detailed local roads and other geographic reference data such as Zip codes and census tract numbers that are not handled by the function 7 15 7 External Data Interface Since the data is now formatted into geographic data structures you can display the objects using di sp aym A Mercator projection is appropriate for small scale regional maps axesm mercator displ aym CL hh displaym H set hh EdgeColor None displaym AL displ aym PL displaym PR displaym SR displ aym RR You can also produce the same map with graphical user interfaces Using the maptool application invoke theml ayers tool by selecting Session gt Layers gt Workspace from the menu bar or invoke ml ayers from the command line by typingrootlayr mlayers ans 7 16 U S Vector Data The amount of detail in the data becomes apparent when you zoom into the federal district of Washington D C While the map has much detail the street patterns contain displaced points and the number of points in the paths of the streets is not enough to give smooth representations of slowly curving streets Pra hy 7 a If you hold down the mouse button on an object you will see its name appear in the lower left part of the figure window All objects have been t
210. s Bureau s Web site at http Awww census gov along with sample TI GER Line files CD ROMs may also be accessible over the Internet through various organizations You can import TI GE R Line data into MATLAB using thet gr ine function Files can be several thousand lines long and reading them may require considerable time and memory Once the data has been read and processed you may want to save the results into a MATLAB workspace MAT file for future use U S Vector Data The following example reads the Washington D C data from the 1994 TI GE R Line edition These files are available over the Internet from The MathWorks at ftp ftp mathworks com and are delivered as text files in a compressed PC Zip archive When extracting make sure the text files are formatted for your computer platform Generally the names of the TIGER Line datasets begin with the string tgr and contain the 5 digit F ederal Information Processing Standards FIPS code for the state and county The dataset for the District of Columbia is TGR1101 CL PR SR RR H AL PL tgrline TGR11001 whos Name Size Bytes Class AL 45x1 112952 struct array Gl 1x1 7444 struct array H 16x1 25030 Struct array PL 64x1 59730 Struct array PR 1x32 53534 Struct array RR 1x8 16632 Struct array SR 1x40 76870 struct array Thet grline function returns Mapping Toolbox geographic data structures for the county line CL primary roads PR secondary road
211. s Lines Hereis the map citylats 30 23 32 citylongs 32 43 116 plotm citylats citylongs r 2 25 2 Displaying Maps In addition to these sorts of permanent geographic data you can also display calculated vector data Calculate and plot a great circletrack from Cairoto Rio deJ aneiro and a rhumb line track from Cairo to Perth gclat gclong track2 gc citylats 1 citylongs 1 citylats 2 citylongs 2 rhlat rhlong track2 rh citylats 1 citylongs 1 citylats 3 citylongs 3 plotm gclat gclong m plotmrhlat rhlong m 2 26 Displaying Vector Maps as Patches Displaying Vector Maps as Patches Vector map data that is properly formatted can be displayed as a patch or filled in polygon Like many Mapping Toolbox functions the names of the patch map display functions can be determined by appending an m to its MATLAB counterpart e g add an m topat ch to get pat chm NOTE The Mapping Toolbox patch display commands differ from their MATLAB equivalents by allowing you to display patch vector data that use NANS to separate faces The following table lists the available Mapping Toolbox patch display functions Function Used to Create fillm Filled 2 D map polygons fill 3m Filled 3 D map polygons in 3 D space patchm Patch objects projected on map axes patchesm Patches projected as individual objects on map axes Theusalo MAT file
212. s a much smaller distance than a degree at the E quator In fact in the first example is 30 N the right mean latitude either The mean position of two points should be equidistant from those two points and further it should be the equidistant point that minimizes this distance Is 30 N 0 a reasonable mean point distl distl distance 30 90 30 0 I 5 5225 dist2 distance 30 90 30 0 dist2 75 5225 5 3 5 Mapping Applications Here is another point call it at on that is also equidistant from both points and the distance is much shorter distl distance 30 90 at lon distl 60 0000 dist2 distance 30 90 lat on dist2 60 0000 What is this mystery point The at is 90 N and any on will do The North Pole is the true geographic mean of these two points Note that the great circle containing both points also runs through the North Pole and a great circle represents the shortest path between two points The Mapping Toolbox includes the function me an m to determine the geographic mean of any number of points This is accomplished through the three dimensional vector addition of all the points For example try the following lats 30 30 longs 90 90 latbar ongbar meanm lats longs latbar 90 longbar 0 This is the answer we now expect This geographic mean can result in one oddity if the vectors all cancel each other the mean is the center of the planet
213. s all the objects on the current map axes An asterisk next to an object indicates that it is visible and an h next to an object indicates that it is currently hidden ZE Object Sets Coastline Parallel _Hide Derete _Zdata Emode Highlight Property Select nternational Boundary and press the Delete button A Confirm Deletion dialog box appears Deleting an object set removes it from the current map axes Press Yes to continue the deletion process The figure now displays only coastlines Change the coastlines from black to blue by selecting Coast ine from the list box and pressing the Property button The Define Object Properties box appears Multiple pairs of property names and values can be entered in this dialog box but you would simply like to change the color of your coastlines from black to blue 6 9 6 Gu Tools Type Color blue in the Object Properties edit box and press Apply Define Object Properties Object Type Line Object Properties eq Color blue Color blue om a The figure now appears as follows a Figure No 1 EE Close the Objects Sets dialog box 6 10 The Complete GUI Environment maptool Zooming in on a Map Display Toget a closer view of the region you will betravellingin you can use the zoom feature of ma pt ool Press
214. s are all formatted geographic data structures containing lines patches or text Thedatainthest at eli ne structureis thesameas that instatepatch but has been defined todisplay as lines rather than patches The structurest at etext contains the corresponding names of the states Note that because of the higher resolution of this data it may require more than the default memory size to display and will take longer to project and render This difference is particularly marked for patches Display the map in an Equal Area Conic projection axesm MapProjection eqaconic mapparallels MapLatLimit 15 75 MapLonLimit 188 60 MLabelLocation 15 MLineLocation 15 PLabelLocation 15 PLineLocation 15 GColor 5 1 1 1 GLineStyle MLabel Parallel south framem gridm mlabel plabel displaym statepatch colormap summer 3 23 3 Atlas Data Here is the result At this scale it is difficult to see the difference between this data and the much smaller us al o workspace By focusing on the Cape Cod region the higher resolution becomes more apparent figure axesm MapProjection mercator Frame on MapLatLimit 41 44 MapLonLimit 72 69 gridm MLineLocation 1 PLineLocation 1 GLineStyle ml abel MLabel Location 1 plabel PLabelLocation 1 displaym statepatch displaym statetext col ormap summer 3 24 United States Vector Data Her
215. s can be obtained from the catalog using the interface function described in the External Data Interface chapter The positions of stars in equatorial coordinates are given in the vectors at and ong These are latitudes and longitudes in degrees for the stars as seen from within the celestial sohere The visual magnitude of each star is given in the vector v mag Stars are typically plotted with diameters proportional to the visual magnitude The vector pvmap contains modified v mag data suitable for display with scat term to exhibit this proportional diameter All magnitudes are positive and brighter stars havea larger pv map number Astronomical Data Display the stars of the northern sky in the E quidistant azimuthal projection axesm eqdazim framem gridm mlabel plabel setmgca Origin 90 180 0 FlatLimit inf 90 MLabel Location 180 15 165 MLineLocation 15 MLineLimit 75 75 MLabel Parallel equator PLabelLocation 15 15 75 GLineWidth 01 GLineStyle scatterm lat long pvmag MarkerSize 0125 You may beabletoidentify the Big Dipper or Ursa Major constellation located at 180 E 60 N 3 31 3 Atlas Data Another system used to describe the positions of heavenly bodies is galactic coordinates This coordinate system puts the center of our galaxy at the origin and places the north pole so that the Milky Way is aligned with the galactic equator The positions o
216. secting Arc B atfix21 latfix22 Line B intersecting Arc C atfix31 latfix32 Arc B intersecting Arc C lonfix onfixll NaN Line B intersecting Arc B onfix21 lonfix22 Line B intersecting Arc C onfix31 lonfix32 Arc B intersecting Arc C Only oneintersection is returned for thelinefrom B with the arc about B since the line originates inside the circle and intersects it once The same line intersects the other circle twice and hence it returns two points The two circles taken together also return two points 5 20 Navigation Usually you have an idea as to where you are before you take the fix F or example you might have a dead reckoning position for the time of the fix see below If you providenavfi x with this estimated position it will choose from each pair of ambiguous intersections the point closest to the estimate Here s what it might look like latfix lonfix navfix latB latB atC lonB lonB lonC 20 14 15 1 0 0 drlat drlon latfix atfixll the only point atfix21 the closer point atfix31 the closer point lonfix onfixll the only point onfi x21 the closer point onfi x31 the closer point A Numerical Example of Using navfix For anumerical example define some specific points in the middle of the Atlantic Ocean These are strictly arbitrary perhaps they correspond to points in Atlantis lata 3 1 lona 56 2 latb 2 95 lonb 55 9 latc 3 15 lonc 55 95 Plot t
217. sed for distance outputs in the toolbox functions An dlipsoid is defined as a rotation of an ellipse around its minor axis Ellipses can be defined with a semimajor and asemiminor axis flattening the parameter n or the preferred method of a semimajor axis and eccentricity The toolbox has functions to convert elliptical definitions from any of these forms to the form of the geoid vector For example the command axes 2ecc returns an eccentricity when given the semimajor and semiminor axes Semiminor Polar Axis Semimajor Equatorial Axis Axis of Rotation The geoid vector along with several other kinds of planetary data for each of the planets and the Earth s moon can be queried using thea manac function provided by the Mapping Toolbox see Measuring the Planets 1 17 I apping Fundamentals 1 18 For the Earth the semimajor axis is about 21 kilometers longer than the semiminor axis Use thea manac function to verify this geoid almanac earth geoid kilometers geoid 6378 14 0 08 semi minor mi naxis geoid semi minor 6356 75 geoid 1l semiminor ans 21 38 When compared to the semimajor axis which is almost 6400 kilometers this difference seems insignificant and can be neglected for most purposes F or this reason most functions in the Mapping Toolbox default to a spherical model of the Earth The ellipse in the previous diagram is very exaggerated Th
218. sentation of geographic data To the ancient Egyptians this representation first took the form of lists of city names in the order they would be encountered when following a given road Two dimensional renditions such as paper road maps are more familiar to us today Even classroom globes are maps under this definition This toolbox addresses electronic representations of geographic data It allows the creation use and presentation of geographic data in a variety of forms and to a variety of ends In the Mapping Toolbox a map is any variable or set of variables representing or assigning values to a geographic location or region from a single point to an entire planet 1 2 Types of Maps in the Mapping Toolbox Types of Maps in the Mapping Toolbox Vector Maps A series of latitude longitude coordinate pairs representing for example points along the coast of Greenland or along Interstate 80 or even the twosets together form a map In this case the geographic data is in vector format and is referred to as a vector map This format consists of specific points along with some indication as to how they should or should not be connected to each other In the Mapping Toolbox vector data consists of sequentially ordered pairs of latitude and longitude coordinates The pairs are considered to be connected in sequence breaks in connectivity must be delineated by the creation of separate variables or by insertingNaNsintothesets at t
219. spect is usually called equatorial rather than transverse True scale Se Correct scale Valued map A matrix map in which entries represent some value or measurement Thet opo workspace contains an example of a valued map Each entry in the matrix map is an average elevation in meters for the geographic position represented by that cell Vector map A map consisting of ordered latitude longitude points possibly connected In the Mapping Toolbox such map data is often represented by two vectors representing latitude and longitude Segments can be separated by the insertion of NaN s in both vectors Waypoint Points through which a track passes usually corresponding to course or speed changes WGS 72 World Geodetic System 1972 An Earth centered datum used as a definition of DMA DEMs presently stored in the USGS data base The WGS 72 datum was the result of an extensive effort extending over approximately three years to collect selected satellite surface gravity and astrogeodetic data available throughout 1972 These data were combined using a unified WGS solution a large scale least squares adjustment A 14 G lossary WGS 84 World Geodetic System 1984 The WGS 84 was developed as a replacement for the WGS 72 by the military mapping community as a result of new and more accurate instrumentation and a more comprehensive control network of ground stations The newly developed satellite radar altimeter was used to de
220. spherical assumption is sufficient This section addresses how the Mapping Toolbox handles more accurate models of the shape or figure of the Earth and other planets What Is a Geoid Literally geoid means Earth shaped The geoid is the precise figure of the Earth Specifically it is an equipotential surface with respect to gravity It is approximately an oblate ellipsoid but not exactly so because of local variations in gravity For the purposes of the Mapping Toolbox the geoid of the Earth is assumed to be an exact ellipsoid This is a simplification of the precise definition of geoid however it is a good approximation which allows a great variety of calculations to be performed that would otherwise be prohibitively complicated Ellipsoidal models of the Earth s figure are very common in practice and are considered sufficient for cartography The use of the term geoid for this ellipsoid is perhaps peculiar to the toolbox Further in the Mapping Toolbox the term geoid is extended to ellipsoidal models for the figures of the Sun Moon and planets 1 16 Geographic Measurement The Geoid Vector Since the toolbox treats the geoid as an ellipsoid the geoid can be described with a two element vector which is often called the geoid vector in this guide The geoid vector has the form semi maj or axis eccentricity The semimajor axis can bein any unit of distance the choice of these units often drives the units u
221. st workspace 1 3 3 3 colorm 6 41 colormap creating for digital elevation map 2 34 colormaps creating with GUI 6 41 menu in maptool 6 4 comet m 2 50 composite maps 1 6 conformal projection 4 3 conic projection 4 5 coordinate transformations 4 14 example using stars 7 39 matrix data 4 16 vector data 4 15 cylindrical projection 4 4 D dcwdata 7 5 dcwdem 7 28 DCW DEM data 7 28 dcwgaz 7 4 dead reckoning 5 31 calculating positions 5 33 rules of 5 32 deg2km1 11 deg2nm 1 24 deg2rad 1 8 degrees notation 1 21 demcmap 2 34 departure 5 5 Digital Chart of the World 7 3 extracting data 7 5 looking up names 7 3 1 3 Index 1 4 reading data files directly 7 13 digital elevation maps DE Ms coloring 2 34 defined 1 4 distance 1 10 distance Seesurface distance distance units convention for navigation functions 5 12 converting between formats 1 24 description of formats 1 24 di stdi m 1 24 dms notation 1 21 dms2deg 1 22 dms2rad 1 22 dreckon 5 12 5 33 E Earth default geoid 1 18 ellipsoid models 1 18 ellipsoid as a geoid model 1 16 converting parameters 1 17 models for Earth 1 18 models for planets 1 19 eqa2grn 5 10 equal area projection 4 3 equidistant projection 4 3 etopo5 7 23 ETOPOS5 mode 7 23 external data sources 7 2 extract m 2 46 F Federal Information Processing Standard FIPS 7 19 7 21 Federal Information Processing System FIPS 7 15 Fifth Fundamental Catalog of Stars 7 36 fill m
222. stics Geostatistics Most statistical functions implicitly assume that the data resides ina Cartesian coordinate system Simply using geographic data in a Cartesian manner can give statistically inappropriate results While the Cartesian assumption may be insignificant for small geographic regions for larger areas it can lead to incorrect conclusions due to faulty distance measures faulty area assumptions or both The Mapping Toolbox provides several functions for analyzing geographic data statistically Geographic Means Consider the problem of calculating the mean position of a collection of geographic points You might beinclined to simply take the arithmetical mean of the latitudes and longitudes using the standard MATLAB mean command but this could be very misleading Take two points at the same latitude 180 apart in longitude for example 30 N 90 W and 30 N 90 E The mean latitude is 30 30 2 30 which seems right However the mean longitude must be 90 90 2 0 From the point of view at the Prime Meridian this seems fine too At the 0 meridian each point has the same longitude difference from the mean What about the point of view at the Date Line At the 180 meridian each point also has the same longitude difference Why isn t 180 the mean longitude This problem is further complicated when some points are at different latitudes Remember a degree of longitude at the Arctic Circle cover
223. struct array The star catalog is processed into MATLAB structures by the external interface function The fields of the structures contain the different types of information for each star while the structure elements represent the individual stars Astronomical Data To view the fields of the structure type the following fk5 1 ans FK5 RAN RAm RAS pmRA DEd DEm DEs pmDE RAh1950 RAm1950 RAS1950 pmRA1950 DEd1950 DEm1950 DES1950 pmDE1950 EpRA1900 e_ RAs e_pmRA EpDE1900 e_DEs e_pmDE Vmag n_Vmag SpType plx RV AGK3R SRS HD DM GC 1 0 8 23 2650 1 0390 29 5 25 5800 16 3300 0 5 47 8770 1 0360 28 48 51 9600 16 3300 43 3100 0 7000 2 33 1 3000 3 1000 2 0600 AOD 0 0240 11 7000 358 BD 28 4 127 7 37 7 External Data Interface If you just want to display the locations of the stars you can find position and visual magnitude data in thestars workspace as part of the Mapping Toolbox atlas data Theremainder of this section illustrates the use of Mapping T ool box functions to manipulate and transform star data for display The star positions are given in terms of right ascension and declination You can display a star map by converting the positions to latitude and longitude coordinates Right ascension is given in hours minutes and seconds while declination is in degrees minutes and seconds hRA fk5 RAh fk5e RAh
224. t contain any functions designed specifically for celestial navigation a simple example can be devised YX W V U T S R Q P 0 N Z A B C D E 6 7 8 9 10 11 1245411410 9 8 4 7 6 5 4 3 2 1 0 1 2 3 4 5 It is possible with a sextant to determine local apparent noon This is the moment when the Sun is at its zenith from your point of view At the exact center longitude of a time zone the phenomenon occurs exactly at noon local time Since the Sun traverses a 15 time zone in 1 hour it crosses one degree every 4 minutes So if you observe local apparent noon at 11 54 you must be 1 5 east of your center longitude 5 37 5 Mapping Applications You must know what time zone you arein before you can even attempt a fix This concept has been understood since the spherical nature of the Earth was first accepted but early sailors had no ability to keep accurate time on ship and so were unable to determine their longitude The engineering exploitation of this scientific truism had to wait until the invention of the chronometer Thet i mezone function is quite simple It returns the description z d an integer for usein calculations a stringz tr of the zone designator and a string fully naming thez one For example the information for a longitude 123 E is the following zd zltr zone ti mezone 123 zd 8 zltr H zone 8 H Returning to our simple celestial navigation example the ce
225. th G Uls Enter a2 in the of Seeds box and a4 in the Value box Press Get and click inside the missed region of Sakhalin Island and inside the Kuril island SSS Figure No 1 Seed Map E Latitude w 5 N 141 142 143 144 145 146 147 148 Longitude of Seeds Yalue E ro ETT 6 39 6 Gu Tools Press Fill In and the values corresponding tothosetwo regions will be changed to 4 The final map appears as follows E Figure No 1 Seed Map EE ja pi 2 T a 125 130 140 145 135 Longitude of Seeds Value reno TT Press the Save button and enter the variable name map to replace the old matrix map of J apan with this new encoded map The Seed Map dialog box can now be closed Constructing Personalized Map Data with G Uls Creating a Personalized Colormap Now you can use the co or m tool to make a custom colormap for your map of J apan To activate thec o or m GUI type col orm map map egend A new figure window displays the map Recall that the values for this matrix map areas follows coastlines 1 J apan 2 water 3 and other countries 4 To change the coastlines to black select 1 from the Codes menu and choose bl ack from the Color menu Next make J apan a light purple by selecting 2 from the Codes menu and choosing cust om from the Color menu The Custom Color GU appears Select a custom color and c
226. the dataset is also available at the sites listed 7 32 G lobal Gridded Elevation Data The data files are named according to towns or features within the quadrangle region If you know the geographic limits of the area you want to map you can look up the names on the USGS Web site or usethe Mapping Toolbox us gs dems function which returns a list of map quadrangle filenames covered by your region Here are the names of the files covered by the Cape Cod maps used throughout this document usgsdems 41 44 72 69 ans providence w providence e chat ham w boston w boston e portland w portland e bat h w The Cape Cod region extends over several of the 1 degree quadrangles Displaying the whole region at the full 3 arc second resolution would require enormous amounts of memory and time Display the region covered by the providence e quadrangle using theus gs dem interface function and a downsampling factor of 5 The resulting map is a 241 by 241 element matrix At full resolution the map would be 1201 by 1201 map maplegend usgsdem providence e 5 map map 0 1 axesm mercator meshm map mapl egend size map map demcmap map lightm 41 5 70 5 material 7 7 1 5 lighting gouraud 7 33 7 External Data Interface This is a zoomed in view of the immediate region around Cape Cod Bay and Martha s Vineyard Global Gridded Elevation Data Zoom in fu
227. the map grid is the set of displayed meridians and parallels Display the grid by setting the map axes property Grid to on This can be accomplished upon map axes creation withaxesm withs et m or with the direct command gridm on Tocontrol display of meridians and parallels set a scalar meridian spacing or a vector of desired meridians in the MLi neLocation property The corresponding property PLi neLocati on serves the same purpose for parallels The default values are every 30 for meridians and every 15 for parallels 9 SQW 150 w 120w 9w eow 3w o 30 E 60E 90E 120E 150 E 180E Default Grid on a Miller Projection By default the grid is placed as the top layer of any display Y ou can alter this by changing theGAItitude property so that other map objects can be placed above the grid The new grid is drawn at its new altitude To reposition the grid back to the top of the display use the command gr i dm reset You can also control the appearance of grid lines with theGLi neStyle and GLi neWi dth properties which are and 0 5 respectively by default 2 15 2 Displaying Maps The Miller projection is an examplein which all the meridians can extend to the poles without appearing to be cluttered Look however at the following Orthographic projections When all the meridians extend to the poles the look is congested The MLi neLi mit property allows you to specify a pair of latitudes at which to ter
228. thers may be drastically different Polyconic and Stereographic azimuthal The classification of the map projections is often a good indicator of whether changes need to be made F or instance switching from a cylindrical toan azimuthal projection requires a few modifications axesm mercator framem on gridm on mlabel on plabel on setm gca Label Format signed 180 150 120 90 60 30 0 30 60 90 120 150 180 2 19 2 Displaying Maps 2 20 To display the default map and frame latitude limits for the M ercator projection type the following getm gca MapLatLimit getmgca FLlatLimit ans 86 86 86 86 Both the frame and map latitude limits are set to 86 for the Mercator projection to maintain a safe distance from the singularity at the poles Now switch the projection to an Orthographic azimuthal setm gca MapProjection ortho What happened to the map frame and labels If you recall the frame latitude limits have not been changed and still correspond to the default values for a Mercator projection as do all the other properties Only those properties that must have particular values are updated for the current projection getm gca FLlatLimit ans 86 86 You must manually reset the frame and map limits to appropriate values for an Orthographic projection so that the circular frame is displayed If you don t know the default or appropriate values provide an em
229. uator in latitude with an orientation of 0 4 7 4 M ap Projections Both of these Miller projections have normal aspects despite having different origin vectors 180 W 150 W 120 W 90 W 60 W 30 W 0 30 E 60 E 90 E 120 E 150 E 180 E 120 E 150 E 180 W 150 W 120 W 90 W 60 W 30 W 0 30 E 60 E 90 E eR B 2 a L 45 S wo 60 S Origin at 0 0 with a 0 Orientation Origin at 0 90 W with a 0 Orientation origin vector 0 0 0 origin vector 0 90 0 This makes sense if you think about a simple true cylindrical projection This is the projection of the globe onto a cylinder wrapped around it For normal aspects this cylinder is tangent to the globe at the Equator and changing the origin longitude simply corresponds to rotating the sphere about the longitudinal axis of the cylinder If we continue with the wrapped cylinder model we can understand the other aspects as well Following this description a transverse projection can be thought of as a cylinder wrapped around the globe tangent at the poles and along a meridian Finally when such a cylinder is tangent along an arbitrary great circle the result is an oblique projection Projection Aspect Here are diagrams of the four cylindrical map orientations or aspects Normal Transverse Cin Pectin Oblique Skew Oblique J iama 4 9 4 M ap Projections
230. uite nicely around the edges of the continents The remainder of this chapter will focus on the fundamental principles of geographic measurement and data manipulation that area prerequisite for creating map displays Chapter 2 Displaying Maps takes up the topic of map display and interaction 1 6 Geographic M easurement Geographic Measurement Latitude and Longitude The position of a point on the surface of the Earth or any other planet for that matter can be specified with two angles latitude and longitude These angles can be specified in degrees or radians however degrees are far more common in geographic usage Latitudeis the angle at the center of the planet between the plane of the Equator and a line through the center passing through the surface at the point in question Latitude is positive in the Northern Hemisphere reaching a limit of 90 at the North Pole and negativein the Southern Hemisphere reaching a limit of 90 at the South Pole Lines of constant latitude are called parallds 490 75 60 45 30 _ Latitudes 15 o yi 430 Lo gitudes B 460 __ 90 I apping Fundamentals Longitudeis the angle at the center of the planet between two planes passing through the center and perpendicular to the plane of the E quator The first planealso includes the surface point in question the second plane contains the Prime Meridian which curre
231. ult As with the world matrix data the low resolution of this data makes it suitable for only large area displays Vector maps are more appropriate where more detail is required Chapter 6 GUI Tools describes how to create higher resolution matrix maps from vector maps This dataset can also be used to determine which state contains a particular geographic point In what state is Alamogordo 32 8990 N and 105 9570 W code tln2val map mapl egend 32 8990 105 9570 code 34 states code ans New Mexico 3 27 3 Atlas Data Terrain As an example of a higher resolution digital elevation map MATLAB provides thecape workspace containing an image of elevation data for the northeastern United States on a 30 arc second grid resolution of about one kilometer or better on the ground The data can be defined as a regular matrix map using thel oadcape function script which rearranges the data and provides the necessary map legend loadcape whos Name Size Bytes Class caption 2x55 220 char array cmap 192x3 4608 double array map 360x360 1036800 double array mapl egend 1x3 24 double array Here we display the elevation data using a conformal Mercator projection so shapes of small regions suffer little distortion while the distortion in relative areas is scarcely noticeable for such a small region axesm MapProjection mercator MapLatLimit 41 44 MapLonLimit 72 69 framem gridm MLineL
232. urface which is then unwrapped into a flat surface Parallels appear as horizontal lines and meridians as vertical lines The following shows a regular cylindrical or normal aspect orientation in which the cylinder is tangent to the Earth along the Equator and the projection is calculated horizontally from the axis Geometric Surfaces A conic projection is derived from the projection of the globe onto a cone placed over it For the normal aspect the apex of the cone lies on the polar axis of the Earth and the surface of the cone touches the globe along a particular parallel of latitude A polyconic projection considers each band of parallels as part of separate cones each tangent to the globe at that particular parallel latitude 4 5 4 M ap Projections An azimuthal projection is a projection of the globe onto a plane For a polar azimuthal projection the planeis tangent tothe E arth at one of the poles with meridians projected as straight lines radiating from the pole and parallels shown as complete circles centered at the pole Each of these projection types can be further modified e Instead of being tangent to one standard parallel the cylindrical or conic surface may cut the globe at two parallels In like manner the plane for an azimuthal projection may intersect the globe instead of being tangent e The vantage point of the projection onto the geometric surface may be changed The perspecti
233. ve may be chosen from the center of the Earth or along the polar axes central or gnomonic from the opposite side of the Earth s surface stereographic or from an infinite point in space orthographic Projection Aspect Projection Aspect Until now the discussion of map displays has focused on the normal aspect by far the most commonly used This section discusses the use of transverse oblique and skew obli que aspects Projection aspect is primarily of interest in the display of maps However this section will also discuss how the idea of projection aspect as a coordinate system transformation can be applied to map variables for analytical purposes The Origin Vector A map axes 0ri gi n property is a vector describing the geometry of the displayed projection The form of this vector is of the following origvec latitude longitude orientation The latitude and longitude represent the geographic coordinates of the center point of the display from which the projection is calculated The orientation refers to the angle from straight up at which the North Pole bears from this center point The default origin vector is 0 0 0 that is the projection is centered on the geographic point 0 0 and the North Poleis straight up from this point Such a display is in a normal aspect In fact changes to only the longitude value of the origin vector do not change the aspect a normal aspect is one centered on the Eq
234. vmag MarkerSize 0125 7 39 7 External Data Interface 7 40 The sky is often depicted in galactic coordinates with the center of our galaxy as the origin of a polar coordinate system You can use the Mapping Toolbox to transform the star positions from equatorial coordinates to galactic coordinates First define the location of the galactic pole and the galactic center galactic pole poleRAhms mat2hms 12 49 0 poleDEhms mat2hms 27 24 0 polelat dms2deg pol eDEhms polelon zero22pi hms2hr pol eRAhms 360 24 galactic center cntrRAhms mat2hms 17 42 0 4 cntrDEhms mat2hms 28 55 0 cntrlat dms2deg cntrDEhms cntrlon zero22pi hms2hr cntrRAhms 360 24 Next create a new origin vector based on the location of the new polein the old equatorial coordinate system Use it to rotate the locations of the pole and the center of the galactic coordinates Note that the origin provided by thenewpol e function results in a system centered on the location of the new pole in the old coordinate system Rotate the star positions and bring the galactic center to zero longitude new origin vector origin newpole polelat polelon rotate our known points newpolelat newpolelon rotatem polelat polelon origin forward degrees newcntrlat newcntrlon rotatemcntrlat cntrlon origin forward degrees rotate the stars glat glon rotatem lat lon
235. will be n choose 2 5 15 5 Mapping Applications The next time you traverse these straits it is a very foggy morning You can t see any landmarks but luckily your navigational radar is operating Each of these landmarks has a good radar signature so you re not worried You get a rangefrom theradiotower of 14 nautical miles anda range from the lighthouse of 15 nautical miles Point A Ce Cape Jones f 4 Point C gions amp Gilligan s Lighthouse PointB Radio Tower Now what You took ranges from only two objects and yet you have two possible positions This ambiguity arises from the fact that circles can intersect twice 5 16 Navigation Luckily your radar watch reports that he has Cape ones at 18 nautical miles This should resolve everything Point A a Cape Jones oa Point C ene di fiX Gilligans xs Lighthouse You were lucky this time The third range resolved the ambiguity and gave you an excellent fix Three intersections practically coincide Sometimes the ambiguity is resolved but the fix is still poor because the three closest intersections form a sort of circular triangle Sometimes the third range only adds to the confusion either by bisecting the original two choices or by failing to intersect one or both of the other arcs at all In general when n arcs are used 2x n choose 2 possible intersections result In this example
236. with the third argument hm for hours minutes the default is hms time2str 13 21 nav hm ans 1313 5 39 5 Mapping Applications GUI Tools An Overview 0 0 0 ee tee 62 The Complete GUI Environment maptool 63 Starting MAP tO ll sms aiia si eta aa aan ed ood er al ater Seba te Rect ee 6 3 The MenuS iie ara e iion e ae a eee 6 4 The Mouse Tool Buttons uussa uaaa 6 4 Activating GUIs with maptool A Working Example 6 5 Constructing Personalized Map Data with GUIs 6 31 Trimming an Existing Data Set 0 000055 6 31 Encoding a Regular SurfaceMap 0 0 cee eee 6 33 Creating a Personalized Colormap 0 200s 6 41 6 G UI Tools 6 2 An Overview The Mapping Toolbox includes a number of graphical user interface GUI tools that provide an alternative to entering toolbox commands from the MATLAB command window The Mapping Toolbox GUIs cover most but not all aspects of the mapping process The Mapping Toolbox GUI system is a collection of independent GUIs most of which can be activated from the command line and or from a map display window at any time during a MATLAB session The Mapping Toolbox also provides mapt ool a comprehensive tool that allows access to most of the toolbox s independent GUIs through a system of figure window menus and buttons Most of the Mapping Toolbox GUIs include a Help button used to enter
237. xample 2 51 T tbase 7 24 TerrainBase model 7 23 text objects editing with Click and Drag editor 6 15 plotting from maptool 6 14 6 24 tgrline 7 14 TIGER Thinned data 7 18 TIGER Line data 7 14 tigermif 7 22 tigerp 7 19 time units conventions for navigation 5 38 converting between formats 1 24 description of formats 1 23 time zones navigational 5 36 ime2str 5 39 i medi m 1 24 imezone 5 36 5 38 issot 2 50 opo workspace 1 5 3 17 topographical maps See digital elevation maps DEMs rack 5 29 6 26 rackl 1 28 1 9 Index 1 10 track2 1 28 2 26 tracks See great circles See rhumb lines trackui 6 16 transformation of coordinate system See coordinate transformation transverse aspect 4 8 trimming data 1 36 6 31 U U S matrix data political 3 26 terrain 3 28 U S vector data low resolution 3 18 medium resolution 3 23 units See angle units See distance units Seetime units usahi workspace 3 23 usalo workspace 2 27 2 44 3 18 usamt x workspace 3 26 UserData property used by the Mapping Toolbox 2 2 2 3 USGS DEM data 7 32 usgsdem 7 33 usgsdems 7 33 V valued maps defined 1 49 vector data calculating intersections 1 34 creating 1 25 1 27 geographic interpolation 1 30 simplifying reducing 1 38 trimming data to a region 1 36 vector maps data format of 1 25 defined 1 3 delineation of objects in 1 25 displaying as lines 2 24 displaying as patches 2 27 volume of planets 1 20 Ww waypoints
238. y other element or set of elements in each vector However the result may be a very crude representation of the original data Another option exists The M apping Toolbox provides a function implementing a powerful line simplification algorithm that selectively deletes points For example reduce the number of points in the state of Massachusetts with ther educem function load usah whos Name Size Bytes Class stateline 1x51 837656 Struct array statepatch 1x51 837758 Struct array statetext 1x51 51190 struct array Thest at el ine structure contains vector data for all 50 U S states and the District of Columbia Weare only interested in the state of Massachusetts the 19th entry in the structure lat stateline 19 lat long stateline 19 long clear state Now simplify your vector data newlat newlong cerr tol reducemlat long whos Name Size Bytes Class cerr 1x1 8 double array lat 958x1 7664 double array long 958x1 7664 double array newl at 253x1 2024 double array newl ong 253x1 2024 double array tol 1x1 8 double array 1 38 W orking with Vector M aps The Massachusetts vector data has been reduced to almost a quarter of its original size size newlat size lat ans 0 2641 Plots of the datasets however show two virtually identical maps original 958 points reduced 253 points 1 39 I apping Fundamentals Most of the reduction has taken place along the straight borders of western

Download Pdf Manuals

Related Search

Related Contents

Philips PerformerPro Vacuum cleaner with bag FC9190/01  Scarica il manuale - INNO    EYE-14  BOLSA DE ELEMENTOS REQUERIDA  Chris Hawryluck - Master of Engineering-User Manual  

Copyright © All rights reserved. Failed to retrieve file