JavaSketchpad® compiler User Manual
Contents
1. The locus objects can t be copied by a transform and can t be used as parent for Point on object No check is done for point P being constructed from M Example draw a parabola A Point 50 400 label d B Point 600 400 AB Line A B F Point 300 320 label F M Point on object AB 0 8 label M FM Segment F M H Midpoint FM hidden P m Perpendicular FM H d Perpendicular AB M P Intersect m d label P parab Locus P M AB 100 The drawn locus changes in real time when moving the base points A B and F Moving point M shows how the parabola is drawn Drawing the locus of a segment ray line is les usefull as it just draws the segment for every position Envelope of line is visible but in a mess of lines Here the enveloppe of m is the same parabola Locus m M AB 100 shows this envelope but draws 100 lines m When a locus has asymptotes spurious lines may appear If n is large enough these lines are just the asymptotes Buttons Buttons trigger actions as show hide parts of the drawing or animate the construction Like measurements they allways have the position x y and the caption parameter HideButton x y text obj obj All the given objects are hidden ShowButton x y text obj obj All the given objects are displayed even if declared hidden MoveButton x y v text A A B B T2. default Helvetica 10 0 0 Angle measurments MeasurelnDegrees 0 in radians default 1 in degrees To reuse a measurement in degrees you must convert it into radian by a Calculate DirectedAngles 0 in Oto m or 180 1 in m to m or 180 to 180 default At last the size of applet is defined by the lt applet gt tag itself width xxx height yyy The parameter codebase jsp defines the location where is stored the Java applet in the directory tree of the site The remaining code GSP class archive jsp4 jar is defined by the specification of JavaSketchpad Summary of items Point NUMX NUMY FixedPoint NUMX NUMY Midpoint SEGM Point on object STRAIGHT CIRCLE POLY NUMB Intersect STRAIGHT STRAIGHT Intersect STRAIGHT CIRCLE CIRCLE Intersect2 STRAIGHT CIRCLE CIRCLE Segment PNT PNT Ray PNT PNT Line PNT PNT Perpendicular STRAIGHT PNT Parallel STRAIGHT PNT Polygon PNT PNT PNT ETC Circle PNT PNT Circle by radius PNT SEGM DIST CALC Circle interior CIRCLE Reflection OBJ STRAIGHT Dilation OBJ PNT NUMB Dilation SegmentRatio OBJ PNT SEGM SEGM Dilation 3PtRatio OBJ PNT PNT PNT PNT Dilation MarkedRatio OBJ PNT CALC RATIO Rotation OBJ PNT NUMB Rotation MarkedAngle OBJ PNT PNT PNT PNT Rotation MeasuredAngle OBJ PNT ANGLE CALC Translation OBJ NUMB NUMB VectorTranslation OBJ PNT PNT Translation FixedAngle MarkedDis
3. is in direction B toward A Intersect is the first and Intersect2 the second along this direction that is Intersect1 is the entry point into the circle and Intersect2 the exit point Similarily with a Ray A B starting from B in direction B toward A and a Segment A B B toward A Drawing horizontal vertical lines Just move the base point through a translation by dx 0 or 0 dy horizontal from A A Translation A 100 0 hidden d Line A A Conditional constructions For instance to restrict a point M in the half plane defined by line d and point P The perpendicular to d from M intersects d in I Line PM intersects d in J may be at infinity Rays IM and JP intersect in M only when P and M in the same half plane from d Continue the construction from this intersection point instead of M line d A Point 100 10 B Point 150 400 d Line A B P Point 200 100 label P M Point 300 200 test C q Perpendicular d M hidden I Intersect d q hidden PM Line P M hidden J Intersect d PM hidden Jp Ray P J hidden Im Ray M I hidden M Intersect Jp Im label M red use M C Point 160 300 label C CM Segment C M points have been moved in the figure and rays made visible in green Segment CM etc exist only when P and M on the same side of d otherwise M and CM disappear and also all furth
4. no local images available Functions on coordinate systems Origin amp Unit UnitCircle AxisX AxisY PlotXY UnitPoint are not available to simplify the compiler as well as aliases DriverPoint and PolarTranslation Option auto is rejected to insure manual start of animations also are options for text styles bold italic plain size number font string justifyLeft justifyRight justifyCenter just to simplify the compiler and option suffix string is rejected for the same reason A more strict check of parameter types is performed by the compiler rejecting constructions that would go through JavaSketchpad with a doubifull result or that would be ignored as meaningless Macros The macros and control structures do not exist in this release of the compiler The preview syntax could be Macro definition define lt name gt type type lt body gt end call id name para para Inside the body the syntax is normal lines except that id names are As parameter 1 2 formal parameters being replaced by real parameters when expanding As id replaced by id with being the number of macro calls The macro returns the last object created display options apply to last object only Example define Bissector pnt pnt s Segment 1 2 hidden m Midpoint s hidden Perpendicular s m end The call d Bissector A B blue e Bissector C D red thick is then expan
5. 2006 Copyright Philippe Chevanne
6. A a 3 hidden AB1 Ray B1 A B2 Rotation MeasuredAngl B1 A a 3 hidden AB2 Ray B2 A C1 Rotation MeasuredAngle C B b 3 hidden BCI Ray C1 B C2 Rotation MeasuredAngle C1 B b 3 hidden BC2 Ray C2 B A1 Rotation MeasuredAngle A C c 3 hidden CA1 Ray Al1 C A2 Rotation MeasuredAngle A1 C c 3 hidden CA2 Ray A2 C draw Morley triangle now D Intersect AB1 BC2 label D E Intersect BC1 CA2 label E F Intersect CA1 AB2 label F t Polygon D E F cyan Triangle DEF is equilateral for any ABC triangle Import Export Importing a source by copy paste from an existing script is nearly automatic just take care of comments and item names ids Ensure there are no multi lines comments nor comments inside comments nor inside or after the code line A name should be explicitely defined for all items in the script The compiler generates a default name if none is given but this could lead to double definitions when modifying the script Also some JavaSketchpad functions are ignored and rejected by the compiler Importing as source a script allready translated by the compiler allways work by construction The primary aim of the compiler is to generate on the fly an applet in the same page as the compiler or automatically exported into a dynamically created page of my site The generated script could as well be exported by copy pa
7. on the stack or put 1 on the stack in addition of A and B is solved by lack of unary minus in contrary from what is written in JavaSketchpad documentation 1 is allways operation then stack 1 Negative values are obtained from x for instance 3 5 is 3 5 or just using substraction instead of addition Geometric transforms Allready constructed items may be copied through a geometric transform The copy has the same type as the original object a segment gives a segment etc Reflection obj straight Objet obj is copied by symetry through line segment or ray straight Dilation obj P k Dilation homothecy centered in P with ratio k gt or lt 1 even lt 0 Dilation SegmentRatio obj P segm1 segm2 Dilation with center P and ratio segm1 segm2 Dilation 3PtRatio obj P A B C Dilation with center P and ratio AB AC Same note as Ratio points prefer 3PtRatio to SegmentRatio if points may collapse Dilation MarkedRatio obj P ratio Dilation centered in P ratio defined by the previous measurement or calculation ratio Rotation obj P a Rotation centered in P with angle a radians Rotation MarkedAngle obj P A B C Rotation centered in P with angle ABC Rotation MeasuredAngle obj P angle Rotation centered in P with angle previously measured or calculated Translation obj dx dy Translation of objet by dx dy dy gt 0 upward VectorTranslation obj A B Translation by vect
8. JavaSketchpad compiler User Manual Preliminary notice This is not the documentation for JavaSketchpad but a user manual of my compiler For the JavaSketchpad documentation see the website of Key Curriculum Press http Awww keypress com sketchpad javasketchpad The syntax is that of my on line compiler The differences from the original syntax of JavaSketchpad will be given in the text For a graphical interface see Key Curriculum Press Summary General syntax p 2 Comments p 2 Code lines p 3 Options p 4 Points p 4 Lines p 5 Circles p 5 Filled items p 6 Measurements p 6 Calculations p 7 Transforms p 8 Captions p 9 Locus p 9 Buttons p 10 Constructions and examples p 11 Arcs p 11 Intersections p 11 Conditional constructions p 12 Using calculates p 13 Import Export p 14 Appendix p 15 Applet options p 15 Summary of items p 16 Functions not available p 17 Macros p 18 Copyright and licence p 19 General syntax A JavaSketchpad drawing is built from the Java applet and the drawing script Inside an HTML page it is defined as lt applet code GSP class codebases jsp archive jsp4 jar width 800 height 500 gt lt param name Frame value 0 gt lt param name MeasurelnDegrees value 0 gt lt param name Construction value edas gt alternate display lt applet gt The Java applet is set by the jsp4 jar file The drawing script by the value of the Construction parameter Other parameters a
9. aces are just ignored also are the trailing spaces 1 A 1A or A define the same name A as A id is optional By default an automatic name is generated by the compiler lt entity gt is the type of geometric item to generate Point Segment Circle etc lt parameters gt Lists of parameters separated by comma and in parentheses depending on entity For instance coordinates of a point center of circle text of a message etc Point 100 200 Circle A B FixedText 20 40 This is just text ShowButton 400 40 Show A B All parameters must be defined before their using Forward references are prohibited In Circle A B points A and B must have been previously defined The element id can be just its rank in the element list A Point 100 200 B Point 100 300 Segment 1 2 isthe same as Segment A B and is replaced by Segment A B inthe source text by the compiler This allows to import existing scripts into the compiler Of course the generated code is allways Segment 1 2 only syntax understood by the applet lt options gt Beween square brackets defines the display options of the element displayed label color etc Point 100 200 label A red Note 1 don t confuse the label what is displayed and the name for referencing in the script A Point 100 200 label B A is the name of the point for further reference like in Segment A B is what is dis
10. ded into 1s Segment A B hidden 1m Midpoint 1s hidden d Perpendicular 1s 1m blue 2s Segment C D hidden 2m Midpoint 2s hidden e Perpendicular 2s 2m red thick which is then translated as usual by the compiler The source of macro definitions is not included in the translated script Control structures Allowed only inside macro definitions if exp exp test on constant value or parameter types no test on variable or measurement if 1 PNT test if param tre 1 is a Point if 1 3 test if param tre 1 is nomber 3 constant not the result of a measurement as this just can t be done at compile time else endif for i parameter list or i value to n by step value n and step could be p constants endfor Copyright and licence JavaSketchpad is the property of Key Curriculum Press Inc its using is granted under the licence conditions defined on their web site http Awww keypress com sketchpad javasketchpad The compiler is my own property grant you the free usage of this compiler from my Web site http chephip free fr in order to generate your own drawings to be published on my site or for your own use In the latter case you should get JavaSketchpad by yourself from Key Curriculum Press Inc This program is distributed as is and without any warranty for damages loss of data or failure of the program Use it under you own liability Version 1 0 creation Jun
11. ed by the default or the given color Polygon A B C Z Defines the polygon from the successive vertices In order A B Z At least 3 points then fills the inetrior of polygon The perimeter couls be used as path for the Point on object and Locus The perimeter is not drawn Use a Circle or a set of Segment to display it These surface items easily play hide and seek and they should use the layer option to define which are in front of others The thick option has no meaning and the traced option would soon fill up the entire plane so they are rejected by the compiler These items may be copied by geometric transforms Measurements and calculations Measurements display the values lengths angles or areas measured on the drawing but they may also be used as parameters in further constructions Every one has the common parameters x y location of measurement on the display text text displayed before the measured value JavaSketchpad allows a suffix after the measured value this is not presently handled by the compiler If they are used just as parameter for further constructions they may be set hidden Parameter value x y text Defines a constant parameter Length segment x y text Length of segment in pixels Distance A B x y text Distance between point A and B in pixels Perimeter Poly x y texte Perimeter of a polygon Circumference circle x y text Perimete
12. er Index of a parameter p1 is named A p2 is B etc Hence a maximum of 26 parameters An operation or state for exponentiation states for negation A function xxxx among sin_ cos_ tan_ asin acos atan sgn_ abs_ rond trnc sqrt ln__ log_ In_ is the natural logarithm base e log_ the base 10 logarithm rond rounds to nearest integer trnc rounds to lowest absolute value integer toward 0 sgn_ 1 0 1 note the 4 characters after the completed by some _ Angles are in radians The reverse Polish notation consists in stacking successive values and consuming the stack during operations Then A B is written AB in reverse Polish notation Put A on the stack put B on the stack sum the two upper values of the stack and put the result on the stack instead B A A A B This notation avoids using parentheses and the applet can execute it just by reading from left to right AB C states for A B C which could also be written as CAB because A B C C A B a last example A B C D is AB CD The results of calculation is finally at top of stack and should be the only thing on the stack Non commutative operations and result into AB A B AB A B and AB A B A exponent B Space characters are ignored but for separate two consecutive numbers For instance 1 2 Ambiguous notation AB 1 as A B then put 1
13. er constructions wich rely on M The same trick intersection with rays or segments could be used in similar cases to ensure what we construct really satisfy the conditions of the problem Conversedly we could extend segments into lines to handle more general cases Some other possibility of conditional drawing is by using Calculate and for instance sgn_ or abs_ to get 0 values if some condition Using calculate All the classical constructions with compass and straightedge are obtained from lines and circles drawn by basic functions The Calculate function allows to go beyond these constructions for instance construct a regular polygon with 7 sides or trisect any angle etc As example let s show the Morley s theorem which requires to trisect angles of any triangle Morley triangle KKEKKKKKKKKKKKKKKKKKKKKHK A Point 100 400 label B Point 400 400 label C Point 200 100 label AB Segment A B BC Segment B C CA Segment C A A BY ET en e a measure angle A and calculate A 3 a Angle B A C 10 10 hidden a 3 Calculate 10 10 A3 a hidden b Angle C B A 10 10 hidden b 3 Calculate 10 10 A3 b hidden c Angle A C B 10 10 hidden c 3 Calculate 10 10 A3 c hidden draw trisectrix B1 Rotation MeasuredAngl B
14. he free points A B are move toward the corresponding points A B at a speed v pixels per frame care of the order destination point AnimateButton x y text A Pa B Pb va vb fa fb ma mb The free points A B are moved along corresponding paths Pa Pb At speeds va vb Points should be on object and move on that object fa fb and ma mb are flags that define the moving fashion f 0 indefinite repeat f 1 once m 0 anti clockwise on a circle back and forth on a line m 1 clockwise on a circle forth only on a line SimultaneousButton x y text obj obj All the buttons obj are acted This allows to declare some v ShowButton hidden and some h HideButton hidden then a SimultaneousButton v h simulateneously shows objects declared in v and hides the objects declared in h Constructions and examples Drawing an arc Draw arc 1 z A Point 100 200 label A B Point 150 300 label B C Point 130 100 label C BC Segment B C hidden M Point on object BC 0 3 hidden P Rotation MarkedAngle B A B A M hidden arc Locus P M BC 100 Ab Ray B A Ac Ray C A The drawn arc is consistent only if angle is less enough than tr Otherwise we have to split it into smaller arcs For instance to draw a semi circle Dra
15. ht from P Turned by 90 clockwise that is t 2 Other lines result from geometric transforms of previously constructed segment ray or line with the same type segment transformed into a segment etc See transforms Circles A circle is defined by the center and one point or the radius resulting from previously known points or measurements Circle center point Circle with given center going through given point Circle by radius center radius Circle with given center and given radius The radius may be a known segment a distance measurement or calculated The compiler rejects a radius which is obviously not a distance area angle slope or ratio are rejected Put them through a calculate at your own risks for the dumb geometric meaning which may result Circles going through three given points should be constructed explicitely The center is the intersection point of two segment bissectors perpendicular from the midpoints That is AB Segment A BC Segment B M Midpoint A N Midpoint BC dl Perpendicular AB M d2 Perpendicular BC N O Intersect dl d2 Circle O A Intermediate items may be declared hidden The compiler doesn t actually handle macros which would allow to define all this as Circumcircle A B C Other constructions in chapter Constructions and examples Filled items Circle interior circle Defines the disk made of the interior of circle It is fill
16. or AB Translation FixedAngle MarkedDistance obj d a_num Translation by previously measured distance d in direction of angle a from horizontal Translation MarkedAngle FixedDistance obj a d_num Translation by distance d pixels in direction of previously measured angle a from horizontal Translation MarkedAngle MarkedDistance obj a d Translation of previously measured distance d in direction of previously measured angle a from horizontal d Distance P Q 10 10 hidden a Angle B A C 10 10 hidden 01 Translation MarkedAngle MarkedDistance 0 a d label O a Copy point O as O in direction defined by angle BAC And distance equals to PQ c a P Captions addition to measurements we can also display any text FixedText x y texte Displays text at location x y on the applet screen The text object defined by this can be copied by PeggedText P obj The text or measurementt object is glued to point P the moves zlong with the point ConcatText x y obj obj The text measurements obj are concatenatedand the resulting text object displayed at location x y Locus Locus P M path n Draw the locus of point P when the free point M moves along the given path which should be a segment ray line circle or polygon M should be previously declared as Point on object and path should be this parent object n is the number of calculated points to draw the locus
17. played on the drawing Of course it is better to put the same to avoid mistakes 2 id is a comment and ignored by the JavaSketchpad applet It is meaningfull only for the compiler Also comments after the may be allowed in the applet but are forbidden in the compiler Also several items on the same line are forbidden Point 100 200 comment Point 150 300 is illegal Options label text Defines the displayed label of a point Only points may have a label The text shoul not contain caracters or look like HTML tags The shall be doubled and to emulate a write black white red green blue yellow cyan magenta preset colors color r g b Any color r g b being red green and blue parts from 0 to 255 hidden Invisible item thick Thick line Only linear items may be thick traced The item leaves a trace when moved Surface items are forbidden layer n Drawing layer increasing for items being above others n 1 to 999 Other options available in JavaSketchpad are rejected by this compiler Points Points may be defined from scratch or result from geometric constructions Point x y Set a movable point initial coordinates x y pixels on the applet x y are limited by compiler to visible area 0 lt x lt 800 0 lt y lt 500 y is downward although y coordinates axis is upward as it should pixel 0 is at top and pixel 499 at bottom FixedPoint x y Set a fixed point that can t be dragged
18. r of circle Radius circle x y text Radius of circle in pixels Area obj x y text Area in pixel of object circle polygon or disk Angle A B C x y text Angle BA BC in radians from t to m The applet allows displaying angles in radians or in degrees the compiler sets this option to radians to comply with other angle values which are allways in radians if anticlockwise from A toward C if clockwise Slope straight x y text Slope of linear object tangent of angle from horizontal Ratio Segments sgmt1 sgmt2 x y text segm1 segm2 Ratio Points A B C x y text AC AB prefer Ratio Points to Ratio Segment if some points may collapse then suppressing the segment from drawing These measures are typed by the compiler it is forbidden to use an area or angle as a radius value for instance Value types Dist lengths distances perimeters Angle angles Area areas Ratio dimensionless values slope length ratio Calc calculated values or constant parameters Calculations The measurements may be used for a calculation Calculate x y text expr p1 p2 pn This calculation is performed from the parameters p1 to pn which should be previous measurments or previous calculations results expr defines the calculation in reverse Polish notation Every part of expr is a2 0 number with optional space to separate from previous numb
19. re used to set background color etc See appendix These applet parameters can t be modifed on line by the compiler Alternate display is in HTML what is displayed instead of applet when the Java engine is not available Every line in the Construction value must comply with the original syntax of JavaSketchpad as specified by Key Curriculum Press It is the result of executing the compiler from the source text which is a different syntax Only the source text format is defined here Allthough very near from the original JavaSketchpad format there are big differences Comments Empty lines are ignored A comment is a line in curly braces Comments spanning on more than one line should have every line enclosed in curly braces The curly braces and the characters are forbidden inside the comment istself Examples This is a comment and this is a comment spanning on several lines blank characters outside the brackets are ignored Code line A code line has the general format lt id gt lt entity gt lt parameters gt lt parameters gt lt options gt and ends with a semicolon lt id gt is the name of the geometric item It can be made of letters numbers or amp 4 or space characters and should not begin with a number or space The and characters are reserved for future meaning Examples A1 A A B A B ABC The leading numbers and sp
20. ste from the translated area of the compiler into your own web page just put it inside a suitable lt applet gt lt applet gt tag You should then download the JavaSketchpad applet from Key Curriculum Press http Awww keypress com sketchpad javasketchpad to be able to view it from your own pages At last the source may be saved by copy paste from the source text area into any text file but as being compatible with the translated script could be regenerated from the script that is available from the view source of the web page You may also use the online compiler to export the drawing itself as a static image from print Screen Appendix Applet options Alltough they can t be modified by the online compiler these options may be used in your own pages Background color default grey 200 200 200 lt param name BackRed value 0 gt lt param name BackGreen value 255 gt lt param name BackBlue value 0 gt Frame Ono frame 1 frame 1 pixel wide solid lt param name Frame value 0 gt Style of labels lt param name LabelFont value gt default Helvetica lt param name LabelSize value 6 100 gt default 12 lt param name LabelBold value 0 1 gt default 1 lt param name Labelltalic value 0 1 gt default 0 Style for buttons idem ActionFont ActionSize ActionBold Actionltalic default TimesRoman 14 0 0 Style for measurements and captions idem MeasureFont MeasureSize MeasureBold Measureltalic
21. tance OBJ DIST CALC NUMB Translation MarkedAngle FixedDistance OBJ ANGLE CALC NUMB Translation MarkedAngle MarkedDistance OBJ ANGLE CALC DIST CALC Length SEGM NUMX NUMY STRING Angle PNT PNT PNT NUMX NUMY STRING Perimeter POLY NUMX NUMY STRING Circumference CIRCLE INTERIOR NUMX NUMY STRING Radius CIRCLE INTERIOR NUMX NUMY STRING Area CIRCLE INTERIOR POLY NUMX NUMY STRING Slope STRAIGHT NUMX NUMY STRING Distance PNT PNT NUMX NUMY STRING Ratio Segments SEGM SEGM NUMX NUMY STRING Ratio Points PNT PNT PNT NUMX NUMY STRING Calculate NUMX NUMY STRING EXPR MEASURE ETC Parameter NUMB NUMX NUMY STRING ShowButton NUMX NUMY STRING OBJ ETC HideButton NUMX NUMY STRING OBJ ETC MoveButton NUMX NUMY NUMB STRING PNT FREE ETC2 AnimateButton NUMX NUMY STRING FREE PATH ETC2 NUMB ETC FLAG ETC FLAG ETC SimultaneousButton NUMX NUMY STRING BUTT ETC Locus POINT STRAIGHT FREE PATH NUMB FixedText NUMX NUMY STRING PeggedText PNT CAPT MEASURE ConcatText NUMX NUMY CAPT IMEASURE ETC Functions of JavaSketchpad not available in compiler Several functions of JavaSketchpad are ignored rejected by the compiler It is forbiden to use the image functions Image ImageOnPoint ImageBetweenPoints as well as the image url option this in the context of on line usage for safety reason no outside url
22. w half circle A Point 100 100 label A B Point 180 200 label B AB Segment A B hidden O Midpoint AB label O pi 2 H Rotation B O 1 5707963267948966 hidden sl Segment A H hidden M1 Point on object sl 0 hidden P1 Rotation MarkedAngle A 0 A 0 M1 hidden arcl Locus P1 M1 s1 100 s2 Segment B H hidden M2 Point on object s2 0 hidden P2 Rotation MarkedAngle B 0 B 0 M2 hidden arc2 Locus P2 M2 s2 100 1 SAAR ARH HH To draw the other semicircle replace 11 2 by 1 2 or exchange A and B Drawing a sector or half disk is not so easy draw a large enough amount of vertices of a polygon Other intersection point When a line d going at A intersects a circle going at A with center O the other intersection point should not be defined using Intersect1 2 because it won t be the right one from the Murphy s law it will be A again The trick is to construct otherwise 0 Point 100 200 label 0 a A Point 50 150 label A D Point 400 30 d Line A D C Circle 0O A second intersection p m Perpendicular d O hidden B Reflection A m label B And similarily for the 2 intersection of two circles Intersection with a ray The choice Intersect1 Intersect2 with a line can be handled as it depends only on the definition of the line Line A B
23. with the mouse Point on object obj k Set a moving point constrained to stay on object obj which shall be a segment ray line circle or polygon perimeter k sets the initial location ratio in segment angle in circle Example AB Segment A B Point on object AB 0 333333 The point is constrained to stay on segment AB initial location is 1 3 of segment from B Other points result from geometric constructions Midpoint segment Midpoint of a segment Intersect straight straight Intersection of two linear items Intersect1 obj circle 1 intersection point of circle with obj which is another circle or a linear item It is hard to know if the desired point is the 1 or the 2 intersection point of two circles Better find other equivallent constructions of that point Intersect2 obj circle 2 intersection point with the circle And also points from geometric transforms of other points see transforms Straight lines Straight lines are defined by two previously defined or constructed points They have direction point2 point1 Segment pointB pointA Defines the segment AB A B Ray pointB pointA Defines the ray AB starting from A p B Line pointB pointA Defines the endless line AB i B Parallel straight P Parallel to the line segment ray straight going through P Has the same direction Perpendicular straight P Perpendicular to line segment ray straig
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