QTPlaut and MatPlaut User Manual
Contents
1. set value to 100 In Start End index set start as O and end as 100 Click Construct In Set orbits to edit set both start and end 48 Triangulate next orbit set 23 to No In Interpolation segments set value to 130 In Start End index set start O and end as 100 click Construct Write a file for MATPlaut Figure 13 H1a closed but mesh tangled at the starting part Figure 14 H1a closed using subset operation 24 Figure 15 H1a closed using local interpolations The user is suggested to study the underlying mechanism This tutorial in some aspects proves the feasibility and usage of local interpolation 4 7 The CR3BP test a complex scenario a b Use QTPlaut to read s L1 s H1 s H1a and s hetH1a Construct s L1 twice Use modify to keep one with LAB 6 10 14 18 22 26 38 Use local interpolation to set orbits 173 interpolated with arclength by 80 segments remember to change the start index to O 4 7 with arclength by 100 segments The other one of L1 only keep LAB 24 Construct H1 Modify it by applying Drop half twice Set mesh and show orbits all Interpolate it with arclength by segments 20 Construct H1a Modify and drop half Interpolate by Reverse Max Arc Div N set N as 80 Set mesh and show orbits none Construct hetH1a Modify and keep only one orbit hide manifold show all orbi2. publishing 11 4 Tutorials 4 1 The coordinate system a b Call an instance of QTPlaut Click Add a solution By the navigation window find the file s xyza Single click the file Then click button Open The file name is shown in the Uploaded solutions combo You can click Detail of a solution to get a brief But this file is not generated by AUTO it is a pseudo solution file for tutorial purpose Then click the Scene tools toolbox header The panel for the Scene tools toolbox is revealed Click the long button Construct a manifold In the Built manifolds combo the solution file name with a unique ID number will be shown In Manifold settings click radio button hide In Show orbits click radio button all In the Diagram panel you can hold the left key and rotate the figure a little bit The figure reveals that the x axis has three orbits the y axis has five orbits and the z axis has seven orbits Whenever you get confused with the orientation of the coordinate system you can load this file Or generate such a file meeting your requirement In QTPlaut the axes and label function are not implemented since MATPlaut or MATLAB can do far better You can try to set Manifold settings as mesh then change back to hide Now use the scroll bar go to the bottom of the Scene tools panel Click Modify a manifold In the right of the panel click drop all In the left p
3. Modify a manifold Drop half select LAB 1 on the left sheet then click Add close YES to save change In Manifold settings choose mesh In Interpolation Settings tick reverse arclength In Archlength segments set value to 100 If you rotate the figure you can see at the starting part of this manifold the mesh gets tangled Now we try to decimate those tangled mesh b Method 1 In Interpolation Settings tick Reverse Max Arc Div N In Draw part of the manifold decrease the End Index until you can t see any lines you don t want You can use the up arrow or down arrow to adjust the End Index Write the scene to file so you can see how it looks like in MATPlaut c Method 2 local interpolation Quit Start a new QTPlaut instance Add a solution file s H1a then Construct a manifold Modify a manifold Drop half then select LAB 90 from the left sheet Add Add LAB 1 after adding LAB 90 At right sheet you need two LAB 90s one LAB 1 at the end In Interpolation Settings tick reverse arclength In Archlength segments set value to 100 In Manifold settings choose mesh Switch to tool box local interpolations Set start orbit and End orbit both to 46 Trianglize next orbit set to No Interpolation Settings tick reverse arclength In Interpolation segments
4. angles set light el as 35 Done 12 The following two figures show the final results in QTPlaut and MATPlaut In this tutorial we try to clarify how the coordinate system is oriented No matter how you rotate the figures right hand rule is always followed We also learn how to cut one solution file into three pieces how to set the tube size and how to change the orbit s color ND PDT CIRC Nag he Figure 1 s xyza in QTPlaut left and in MATPlaut right 4 2 The closed hex prism a In QTPlaut add solution s hexprism This file should be in the unzipped QTPlaut folder or in the sample_files folder b In scene tools Construct a manifold In Manifold settings choose mesh Modify a manfold Drop all Add all Select LAB 1 if you click or highlight any cell for the line of LAB 1 that means selected close YES to save change In Interpolation Settings click arclength or reverse arclength in Interpolation segments change Arclength segments to 5 Write the scene to a file named hexprism mlf Close QTPlaut a Not closed b Closed c Closed and Interpolated Figure 2 s hexprism in QTPlaut 13 read hexprism mlf in MATPlaut Change light polar angle el to 35 In the Manifold color settings try the three different options You can also try with other colormap options manifold alpha value view angles light angles an
5. be seen immediately without the restarting of the program In your MATLAB command console change the working directory to the directory where you unzip the MATPlaut files In the command line type MATplaut The GUI is started The out looking likes the QTPlaut but MATLAB is not specialized at GUI design It has only limited controls However it meets our requirement 3 2 1 Input mlf file In text input line enter the full path file name xxx mlf MATLAB GUI doesn t offer a navigation window to help you to find the file If you just enter the xxx mlf MATPlaut will try to retrieve the file from the directory where you call MATPlaut 3 2 2 Current Solution In the combo box there will be the indices list of the solutions you wrote to the mlf file The original solution file name of the current index with a unique ID will appear on the right The following settings till camera motion will affect the current solution only We should say affecting the current presentation of a solution 3 2 3 Manifold color setting The solution of AUTO s 3D 2D projection can be mapped onto a rectangular One edge dotted by the indices of orbits one edge dotted by time or arc length Colormap is a sequence of colors we can use to enhance the contrast So you will understand the difference between colormap onto arc length or colormap onto orbits indices Single color means only one color for the manifold If you tick this option you can cli
6. color settings group box As discussed above 3 1 2 11 Interpolation settings group box none It doesn t mean nothing It means no interpolation the original orbits mesh are kept time Along the evolution of time each orbit of the manifold is interpolated by n segments of time into n 1 points n is set by a spin box the Time segments in the group box interpolation settings below arclength Along the evolution of time each orbit of the manifold is interpolated by n segments of arc length into n 1 points n is set by a spin box the Arclength segments in the group box interpolation settings below reverse time Reverse to the evolution of time each orbit of the manifold is interpolated by n segments of time into n 1 points n is set by a spin box the Time segments in the group box interpolation settings below reverse arclength Reverse to the evolution of time each orbit of the manifold is interpolated by n segments of arc length into n 1 points n is set by a spin box the Arclength segments in the group box interpolation settings below The following options set a segment scale rather than set the number of segments In a solution we can always find the maximum or minimum arc length or the maximum or minimum time So the step of interpolation can choose a uniform scale for all the branches orbits such as the max arc length divided by n The interpolation always keeps the first point and the end point of a branch n is alway
7. halfhalforbits 1 s17 revarc100 halfhalforbits 2 Figure 7 s 17 plotted by MATPlaut 1 19 s17 revarc50 halfhalforbits 1 s17 revarc50 halfhalforbits 2 s17 revarc20 halfhalforbits 1 s17 revarc20 halfhalforbits 1 Figure 8 s 17 plotted by MATPlaut 2 20 4 5 The CR3BP mu 0 063 H1a and hetH1a This tutorial needs results of AUTOO7p demo r3b d Call an Instance of QTPlaut Add a solution with file s hetH1a and Add a solution with file s H1a Switch to tool box Scene tools in Uploaded solutions select s hetH1a Construct a manifold Modify a manifold Drop all select LAB 34 close YES to save In Manifold settings tick hide In Show orbits tick all In Uploaded solutions select s H1a Construct a manifold In Built manifolds select s H1a 1 You select to see s H1a as mesh or vertices Write the scene to a file as h1a m hetH1a o full mlf In interpolation settings select reverse arclength in Interpolation segments set Archlength segments as 100 Write the scene to a file as h1a m hetH1a o revArc100 mlf In interpolation settings select reverse arclength in Interpolation segments set Archlength segments as 50 Write the scene to a file as h1a m hetH1a o revArc50 mlf In interpolation settings select reverse arclength in Interpolation segments set Archlength segments as 20 Write the scene to a file as h1a m hetH1a o revArc20 mlf Close QT
8. Camera Motion 3 2 12 Light Motion 3 2 13 Light 3 2 14 Light and camera polar angles Please check MATLAB documents for view and lightangle commands 3 2 15 Input r3b file s start In order to present the CR3BP more accurately we parse the L1 L2 L3 L4 L5 positions and mu thus the primaries positions from the s start file It is the user s responsibility to provide the correct s start file corresponding to the solutions we are dealing with 10 3 2 16 Earth size 3 2 17 Moon size They are resizable But the value should be none zero If they are positive the larger primary will use the earth texture the smaller primary will use the moon texture For other CR3BP problem the sizes could be set negative thus no textures are shown 3 2 18 Liberation point size We use some cubes to represent the liberation points There are resizable 3 2 19 Disk Alpha 0 1 0 Change the transparency setting of the CR3BP disk on the orbiting plane 3 2 20 CR3BP Mu L1 L2 L3 L4 L5 positions are acquired from s start mu is acquired from the second line of the first branch of the s start file The large primary is at mu 0 0 the small primary is at 1 mu 0 0 3 2 21 Build a m script Suppose you write a test1 m file to your MATLAB working directory You may call it by type test1 in your MATLAB command line console What will you get The MATLAB gurus then can change the axes add labels export the image file and etc for their
9. Plaut Call MATPlaut Try file h1a m hetH1a o full mlf In Current solution select 2 for s H1a 1 In Manifold color settings select colormap onto orbits indices In Current solution select 1 for s hetH1a O In Tube size change it to 0 02 Orbit Alpha change the value to 0 3 In Input r3b file enter s start if this file is not in the MATLAB working directory the user should enter the full path name Click read The figure now looks like the one on the cover Try other files At the GUI right bottom Build a m script input file name testr3b m then click write close the GUI In MATLAB command line type testr3b you will see a same figure as plotted through the GUI Then you can change the script yourself or add labels change axes export the figure and etc Figure 9 CR3BP h1a m hetH1a o full mlf 21 Figure 10 CR3BP h1a m hetH1a o revArc100 mlf Figure 11 h1a m hetH1a o revArc5O mlf 22 r Figure 12 h1a m hetH1a o revArc20 mlf 4 6 The CR3BP close manifold H1a You may notice in tutorial 4 5 There is a gap in manifold H1a We try to close this gap in this tutorial There is no mathematical proof that the map should be closed or not Here we just want to show that QTPlaut has such a function a Callan instance of QTPlaut Add a solution file s H1a then Construct a manifold
10. QTPlaut and MatPlaut User Manual Beta version The AUTO solution interpolating and plotting program package Zhikai Wang Concordia July 1 2008 This project is sponsored by Prof Eusebius Doedel Computer Science Department Concordia University Canada Contents 1 2 3 5 MUOU GION ao 2 InspaNatron anti SSEUD N E cet eb PPS Eb EM vec desis DEED dM MEME LII MM UM 2 WITS OTC CLOTS orate teciny Emo TO oon 3 3 1 OVP AIG e E 3 3 2 MATEU scrsdcascceceasesatiee cogntncecdenmneneausnnvaasd uses curntose cou esuattonsencanadt 9 DUO m 12 4 1 The coordinate SUBEGIT nde E eHRtS oiRIDN IE Itibs vnu EIU oM vM UR UU MM MEM CR INN DEI EUE 12 4 2 Ella Neleci od eei a NN OO m m 13 4 3 Interoolatioh abd Me eee eee ne ae te ante one ciu DIE ra UMS nme Uem ERU IU MM ERE 14 44 Thebore nzmanifold 5iimeksersn neri tk ev NN n ER bx RE Ede Ra CURES REP kir Sic ME A EE ERE Eine 16 4 5 The CR3BP mu 0 063 H1a and hetH1a This tutorial needs results of AUTOO7p demo r3b 21 4 6 The CR3BP close manifold ALS eese ioter redet sees o bue ette uoa ete e ba eroe ee ert o eru etat bent et eo feeder ides 23 DOT KS areas year ia vars casei rye csv le Ima mance ea crea DV INVENI MEDII SU C EVE 28 im Introduction The QTPlaut is a program that can read multiple AUTO solutions The soluti
11. TEE Bi SSN gt 211 WWW 3 WwvvvvvvYvvv Sg Ws S s z WW OSS VNVVVVV lt MVM 3 Figure 4 Tutorial 4 3 Interpolation and Mesh 15 Max Time Div N 20 Reverse Max Time Div N 20 Min Time Div N 20 Reverse Min Time Div N 20 This tutorial explains the various interpolation options and their mesh constructions 4 4 The Lorenz manifold a Open an instance of gtplaut Add a solution file s 17 File s 17 is an AUTO solution computed by Prof Eusebius Doedel for the famous Lorenz manifold This file should be in the example files folder Its size is about 62 5MB There is a smaller arc length solution s 15 You may also try with this solution Construct a manifold You may switch Manifold settings between vertices and mesh but the vertices option seems to be better In the Diagram transformation slide the first two bars to the left end use the fourth bar to zoom the diagram Write the scene to a file as s17 full mlf it will take a while QTPlaut can process very large file the developer once loaded around 1G bytes solution files in a PC with 8G main memory Fedora 8 1386 64 Your free memory should be at least twice the size of the files you plan to read b In nterpolation Settings tick reverse arclength in Interpolation segments field Archlength segments change 20 to 100 Write the scene to a file as s17 revarc100 allorbits mlf in Interpolation segments field Archle
12. TPlaut is divided into two parts On the left is the plotting panel On the right is the toolbox panel The toolbox feature of QT4 makes possible large number of controls in a limited panel space 3 1 1 Solutions tools tool box The solutions tools have four controls 3 1 1 1 Add a solution button By clicking this button you can be navigated through a window to locate an AUTO solution file 3 1 1 2 Uploaded solutions combo box You can load multiple solutions All loaded solutions can be show in this combo box Each solution has a unique ID which is not shown explicitly For each branch only the branch header and the next NTPL lines are kept 3 1 1 3 Drop a solution button Click this button to drop the current item shown in combo 3 1 1 2 3 1 1 4 Detail a solution button Prompt a dialog of table showing the brief of the current solution 3 1 2 Scene tool tool box This tool box contains controls to build plot and interpolate a manifold In QTPlaut a manifold is a 2D or 3D projection of an AUTO solution It is simple A scene presents one or more manifolds Although a solution can be loaded more than once it is not advised If a manifold needs interpolation operations it will be reconstructed from the raw solution data loaded so a solution should always be kept after it is loaded Both the manifolds and the solutions have their unique IDs The manifold ID is shown explicitly in the built manifolds combo The current manifold or
13. anel select items with LAB 1 2 3 This is like in a spread sheet software You hold shift key to select sequentially ctrl to select continually Then click Add Close the dialog Click Yes to confirm the changes Now only the x axis are shown Click Construct a manifold again In the built manifolds combo there will be two items Highlight s xyza 1 The unique ID start with zero hide manifold Show orbits all Click the Modify a manifold again Drop all Add LAB 4 5 6 7 8 Close YES to save changes Construct a s xyza 2 repeat k but add LAB 9 10 11 12 13 14 15 You can try to see the mesh s But remember to hide again for each manifold Click Write the scene to a file Change the file name to axes mlf Click save Close QTPlaut Go to MATLAB Call MATPLaut clear all and add axes mlf at the add mlf file edit line You should add the full path name or copy this file to your working directory The current solution index should be 1 and name s xyza 0 At tube size clear all and type 0 05 as the new tube radius hit enter Then click Set orbit s color You can choose a color you believe it is red Select index 2 for s xyza 1 change the tube size and set the green color for it Do the same thing with index 3 for s xyza 2 set color as blue The green orbits may not shine In the camera and light polar
14. ck the set manifold color button to change the color 3 2 4 Color map All these thirteen color maps are cited from MATLAB So please check the MATLAB documentation for details 3 2 5 Set Manifold Color As stated above if a manifold is set to be single color the color can be changed here through a very convenient color palette GUI 3 2 6 Set orbits color If in QTPlaut you allow the plotting of orbits the orbits all share one color and the color can be changed here Among these orbits if you want to highlight one or more with different colors you may construct multiple manifolds from a same solution Modify the manifolds to get the orbit orbits you want to highlight then set different colors here 3 2 7 Orbit style Obviously tube option gives better visual effects But line option is simple and fast to be plotted 3 2 8 Tube size You can edit the tube size in the first text field The input should be positive number Fault correction is implemented here The second text field is the delta you click the button the tube size will be increased or decreased by delta but always be greater than zero 3 2 9 Manifold Alpha The fault correction trigger will always guarantee the alpha value is bounded by 0 1 0 O means the manifold is totally transparent or invisible 1 means it is opaque or no light could penetrate 3 2 10 Orbit Alpha It is convenient to set different alpha values for orbits and manifold respectively 3 2 11
15. d etc The scale in MATPlaut is different from QTPlaut In QTPlaut the figure is scaled into a cube In MATPlaut we use daspect 1 1 1 For daspect please check MATLAB manual a HSV mapped onto arc length b HSV mapped onto orbits indices c Single color Figure 3 s hexprism in MATPlaut the alpha value is 0 5 In this tutorial we try to close a manifold if the user believes the solution should be of a cylinder a tube or a torus type We also try with simple interpolation settings apply different color schemes and the user can use this naive pseudo solution to explore all kinds of settings 4 3 Interpolation and Mesh d Add a solution file s intpl Construct a manifold In Manifold settings set mesh In Diagram transformation use the slide bars to rotate and zoom the diagram that fits best In Scene tools groupbox Manifold color setings set Single Click button Set Manifold Color choose a color that fits best In Interpolation Settings choose different interpolation settings Since the pseudo solution we built has linear time space relation the difference between time and arc length interpolation is not obvious In the next tutorial the users can experiment it by themselves 14 3 5 NANA Ref E S cem MAN BONN RN NM a S o D PI AAA E Tei VUA S Z E E 1071 WI eV ir UN c ccc MM S Hi Si S a AAA lll E Ne x
16. in the solution are shown 0 is always for time t 1 2 3 are as the sequence in AUTO solution 3 1 2 4 Construct a manifold button Construct means project the current solution according to the dimension settings into 2D or 3D graphical representation the manifold Each manifold has a unique mother solution A solution can have multiple presentation of manifolds drawn as orbits only manifold only both or part of them By default the manifold is plotted using color map HSV onto its orbits indices In short it is marked as diverse A manifold present itself as the manifold vertices mesh surface or the orbits showing all or single A subset operation is possible by setting starting end orbits and starting end indices The manifold can be single colored or diverse colored So the orbits can also be single colored or divers colored 3 1 2 5 Built manifolds combo box Showing the current manifold It contains all the built manifolds with the unique IDs starting from zero 3 1 2 6 Drop a manifold button Drop the current manifold in the built manifolds combo 3 1 2 7 Set Manifold Color button If the Manifold color settings below are chosen as single a dialog will be prompted so you can choose the color 3 1 2 8 Set Orbit Color button If the Orbits color settings below is chosen as single a dialog will be prompted so you can choose the color 3 1 2 9 Manifold color settings group box As discussed above 3 1 2 10 Orbits
17. ite the scene to a file button What you see will be what you write to the mlf file A solution s projection can be written to the mlf as the manifold the orbits or both If the manifold settings is hide the manifold in MATPLaut the surface won t be written If the show orbits is set as none the orbits won t be written you won t see those tubes But all orbits or single orbit has no difference they all mean write all orbits In mlf there always are The total number of the solutions projections For a manifold the list of all vertices the list of triplets of how they are triangulated the indices of the stripes Stripe means the triangles between two orbits MATPlaut needs it to apply colormap schemes For orbits if shown there is the list of end vertices indices of each orbit and is also the total number of orbits written Some tutorials at the end of this document will help to understand 3 1 3 Local interpolations If the user needs to interpolate some specific orbit or some sequential orbits the user can use local interpolation 3 1 3 1 Built manifolds Show the current manifold 3 1 3 2 Available orbits Show the indices of all the orbits 3 1 3 4 Set orbits to edit Select start or end orbit part to edit If start end only one orbit is selected 3 1 3 5 Triangulate Next Orbit By default during triangulation each orbit is triangulated with the next orbit the end
18. ngth segments change 100 to 50 Write the scene to a file as s17 revarc5O allorbits mlf in Interpolation segments field Archlength segments change 50 to 20 Write the scene to a file as s17 revarc20 allorbits mlf c Modify a manifold then Drop half close YES to save changes In Interpolation Settings tick reverse arclength in Interpolation segments field Archlength segments change to 100 Write the scene to a file as s517 revarc100 halforbits mlf Archlength segments change to 50 Write the scene to a file as s17 revarc50 halforbits mIf Archlength segments change to 20 Write the scene to a file as s17 revarc20 halforbits mlf d Modify a manifold then Drop half close YES to save changes In Interpolation Settings tick reverse arclength in Interpolation segments field Archlength segments change to 100 Write the scene to a file as s17 revarc100 halfhalforbits mlf Archlength segments change to 50 Write the scene to a file as 17 revarc50 halfhalforbits mlf Archlength segments change to 20 Write the scene to a file as s17 revarc20 halfhalforbits mlf Close QTPlaut e In MATPlaut try to open and plot these files respectively It is good to restart MATPlaut each time f However MATLAB failed to plot the following files S17 full mlf s17 revarc100 allorbits mlf s17 revarc5O halforbits mlf s17 revarc20 allorbits mlf s17
19. ons can be interpolated by the Lagrange interpolation method The interpolated results can be put together into a mlf file The core of QTPlaut is the interpolations or simplifications by GUI Such operations are possible by the frequent usage of dynamic memory allocation of templated C programming The MatPlaut is a combination of MATLAB m files that plot the mlf generated by QTPlaut Again it utilizes object oriented programming techniques But it is implemented with the MATLAB OO programming The great feature of MatPlaut is the transparency effects while plotting multiple manifolds or complex manifold We may say to present the 2D or 3d projections of one or more AUTO solutions An AUTO solution usually contains large quantity of data To simply them with MATLAB script program doesn t seem to be practical The plotting functions like surf or patch also have limited data processing ability So we have to turn to C memory management As long as the main memory of the operation system permits we have a container to put the reactants The dynamic memory allocation makes possible the processing of a solution file without knowing in advance the number of branches it contains how the mesh is set and even how many solutions we want to put in the same scene There are many packages that can implement the amazing transparency effects But the MATLAB plotting functions are the easiest to program with With them we save huge q
20. orbit will do nothing The trick here is that you add an orbit twice use the setting here not to be triangulated with itself Then the orbit can have two interpolation settings So it can help to form better triangle mesh when the two other orbits at either side of it have a big difference in arc length 3 1 3 6 Interpolation settings Explained in 3 1 2 3 1 3 7 Interpolation segments Set n for interpolation 3 1 3 8 Subset operation construct append Suppose you set n as 100 you will get 101 points for the interpolated orbit orbits Construct create a new orbit with vertices start end bounded by 0 100 Append takes the start end part bounded by 0 100 adds them to the end of the orbit orbits you select This trick makes it possible that one orbit can have more than one interpolation settings The append feature is not fully tested 3 1 4 Diagram transformation The first slider rotates the scene about the OpenGL x axis The second slider rotates the scene about the OpenGL y axis The third slider rotates the scene about the OpenGL z axis The fourth slider performs some limited zoom operations The mouse can perform some rotation operations Since MATPlaut can do far better in transformations this part is kept as simple as needed 3 2 MATPlaut MATPlaut is a set of MATLAB m files It has a GUI for the users to ease the settings for plotting AUTO solutions The GUI is event driven So the effect of setting change can
21. raw part of the manifold group box If a manifold has N orbits A subset operation is possible by select the start end orbits bounded by 1 N Combing the starting end indices setting we can take a patch from a manifold The indices are bounded by 0 M M is the maximum vertices count of all orbits 3 1 2 14 Orbit style group box Tube or line In fact in QTPlaut all orbits are drawn by line But one is anti aliasing the other is not 3 1 2 15 Orbit settings group box Current orbit If you set show orbits as single This index decides the current orbit you see Tube size line size vertex size settings are useful to highlight part or the whole manifold in QTPlaut without transparency effects in QTPlaut 3 1 2 16 Modify a manifold button This is another powerful tool to select orbits from manifold It uses spread sheet type dialog The user can drop duplicate re sequence the orbits against the original solution At the end another dialog will popup Remember YES is to save the change NO keep the original before you call the modification The difference with the draw part of the manifold is that draw part doesn t delete the orbits from the manifold any interpolation operations still applies to all the orbits The result of modifying the manifold will remove or reset the orbits irrecoverable To restore the original orbits the user should drop the modified manifold and construct it from the solution again 3 1 2 17 Wr
22. revarc100 halforbits mlf s17 revarc5O allorbits mlf The experiments are done on a Pentium IV machine 2G memory Windows XP SP2 In next tutorial we can eve plot file size greater than some of the above The reason could be during rendering transparency effects MATLAB puts some limits on the total number of vertices or the maximum layers of graphical objects to test the depth or the maximum number of textures it can mix In OpenGL QT we can plot unlimited graphical objects in theory But to implement the transparency effect the OpenGL programming job is so huge and it involves too many computer graphics techniques In this tutorial we have in some senses tested the limit of QTPlaut and MATPlaut By following the tutorials explored by the developer the users can achieve a practical visual presentation of their mathematical solutions 16 revarc50 allorbits s17 s17 revarc100 fullorbits eye di CPU eis rd Ns ra ANS A MN TT ded 22 22 a ne revarc50 halforbits s17 s17 revarc100 halforbits revarc20 allorbits s17 s 17 interpolated and plotted by QTPlaut 1 Figure 5 17 Medi Yes f ve SF s17 revarc20 halforbits s17 revarc100 halfhalforbits s17 revarc50 halfhalforbits s17 revarc20 halfhalforbits Figure 6 s 17 interpolated and plotted by QTPlaut 2 18 s17 revarc20 halforbits 1 s17 revarc20 halforbits 2 s17 revarc100
23. s greater than 1 so the resulted manifold orbit will always contain at least two points A branch that contains only one point should be avoided while AUTO solution s NTPL is always 2 But for example in the CR3BP L1 family has some branch points shrink into one point So the Lagrange interpolation has overlapped mesh points and divides zero QTPlaut can deal with this case by decimating the redundant overlapping points The uniform scale interpolation such as Max Arc Div N or Min Arc Div N is very fit for the simplification of the CR3BP L1 family type The outer orbit will contain more points and the inner less So the resulted mlf s size will be optimized All the interpolation settings are global affecting all the orbits But if you interpolate the only one single branch or part of the branches QTPlaut will set the option to local interpolation or no change In some extreme cases the user may need to interpolate some specific orbits to achieve better visual effects QTPlaut offers such functions that will be shown in 3 1 3 3 1 2 12 Interpolation segments group box Set n for time or arc length interpolation respectively 3 1 2 13 Manifold settings group box Hide The manifold is not shown Thus the manifold will not written to the mlf file In QTPlaut what you see is what passed to MATPlaut Vertices show manifold as vertices Mesh the net mesh after triangulation Surface it is left for future improvement 3 1 2 13 D
24. solution is the current item in according combos About the dimensions in MATLAB x axis orients from the left to the right of the screen y axis orients as the direction as the user s eye vector pointing at the screen z axis from the screen bottom to the top But in OpenGL this is not the case The x axes are the same in openGL the y axis is from the screen bottom to the top and the z axis is a vector orthogonal to the screen but pointing to the user The above describes the case that view vector is the user screen vector without any transformation In QTPlaut we keep the same axes orientation as MATLAB So in the dimension settings group box X means the openGL X equal to the real world X dimension 1 in solutions dimension O is always the time t Y means the OpenGL Y equal to the real world Z dimension 3 in solutions Z means the OpenGL Z equal to the real world Y dimension 2 in solutions In the case of 2D X axis originates from left to the right of the screen and Y axis originates from the bottom to the top of the screen No matter how tricky the transformations are right hand rule is always kept 3 1 2 1 Uploaded solutions combo Showing all the solutions loaded highlighting the current solution we are working with 3 1 2 2 Plotting dimensions group box Two exclusive radio buttons 2D or 3D 3 1 2 3 Dimension settings group box The orientation is discussed as above In each of the three combos all dimensions
25. ts Write the scene to a file Close QTPlaut Have a look at the file size comparing the s Files In MATPlaut try to see if you can set the figure as the following 25 26 Figure 16 The CR3BP test a complex scenario 27 5 Remarks 1 AUTO a software for continuation and bifurcation problems in ordinary differential equations Eusebius Doedel http cmvl cs concordia ca auto 2 QT across platform application framework http www trolltech com 3 MATLAB The Language of Technical Computing http www mathworks com products matlab 4 The earth texture land ocean ice 2048 jpg NASA 5 The moon texture moonmap1k JPG http planetpixelemporium com earth html 6 The files followed QT examples are stated in file headers While the remaining part can run independently by C OpenGL IOs 7 All MATPlaut codes follow MATLAB help document 28
26. uantity time than program with OpenGL or Open Inventor and etc Installation and setup The QTPlaut needs openGL Mesa and QT Please make sure their libraries are installed in the target machine The QT version 4 3 4 is used for QTPlaut development Unzipping the QTPlaut zip gz to a folder called qtplaut The folder name can be changed but the execution file built would have the exact name of this folder After changing directory under this folder xxx in a Linux terminal or a MS Windows DOS shell you type qmake project Then you open the xxx pro file and add a line QT opengl casesensitive Save the file then type qmake without any arguments In Linux you can use make in MS Windows Visual C you can use nmake to build the executable Its name will be xxx same as the folder name Normally you have to add the following lines in your Linux bashrc PATH usr local Trolltech Qt 4 3 4 bin SPATH LD LIBRARY PATH SLD LIBRARY PATH usr local lib usr local Trolltech Qt 4 3 4 lib export PATH export LD LIBRARY PATH But they are the issues of QT installation while not those of QTPlaut The installation of MatPlaut is rather simple Unzip the files to your working directory The MATLAB version should be 7 5 0 R2007b the functioning of earlier versions is not guaranteed 3 Instructions 3 1 QTPlaut You can call the QTPlaut program by clicking the executable directly or call from terminal command The main Window of Q
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