1mathsPIC(1)                 General Commands Manual                mathsPIC(1)
2
3
4

NAME

6       mathsPIC
7

AUTHORS

9       A. Syropoulos and R.W.D. Nickalls (April 26, 2010)
10
11        asyropoulos[at]<yahoo><com>
12        dick[at]<nickalls><org>
13
14

DESCRIPTION

16       mathsPIC  is  a  Perl  filter  program for PiCTeX. mathsPIC has its own
17       macro and macro library capability, and allows use of mathsPIC, PiCTeX,
18       TeX  and  LaTeX  commands. A significant feature of mathsPIC is that it
19       allows access to the command-line, and so allows  the  user  to  extend
20       mathsPIC commands by calling Perl and other programs written to perform
21       particular drawing actions. See the package manual for full details and
22       examples. The latest version can be downloaded from
23
24       CTAN: tex-archive/graphics/pictex/mathspic/perl
25
26       Commands  which  can be used in the mathsPIC script file fall into four
27       main groups (a) mathsPIC macro commands (prefixed with %def), (b) regu‐
28       lar  mathsPIC  commands  (do  not have a backslash), (c) regular PiCTeX
29       commands (all have a backslash), and (d) regular TeX and LaTeX commands
30       (all have a backslash).
31
32       The  following  mathematics functions can used (note that decimal frac‐
33       tions having an absolute value less than 1 must have a  leading  zero).
34       Note also that all the trignometric functions require their argument in
35       radians.
36
37       Trigonometric: sin(), cos(), tan(), asin(), acos(), atan()
38
39       Remainder: rem(); eg var  r=12 rem(5)
40
41       Integer: int(); eg var  r= int(3.87) --> 3
42
43       Sign (returns -1, 0, +1): sgn(); eg var  s=sgn(-3.27) --> -1
44
45       Square root: sqrt(); eg var s = sqrt(14)
46
47       Exponentiation: **; eg var j = r**2
48
49       Pi constant (3.14159...):  _Pi_  and  _pi_
50
51       e constant (2.71828...):  _E_  and  _e_
52
53       Linethickness:  _linethickness_  ; eg  var t = _linethickness_
54
55

COMMAND-LINE USE

57       perl mathspic.pl [-b] [-c] [-h] [-o  <outfile>]  <infile>
58
59       -b enables beep if mathsPIC detects an error
60
61       -c disables the writing of comments to output file
62
63       -h displays the help file
64
65       -o defines the output file name
66

MACRO COMMANDS

68       macro definition commands are prefixed with %def and can  take   either
69       0,  1,  or  more parameters. Macros will generally be used as part of a
70       var command as shown below. Macros are deleted using  the  %undef  com‐
71       mand.
72
73        -----syntax:
74        %def MACRONAME(parameters)<macrodefinition>
75        %undef MACRONAME(parameters)
76
77        -----notes:
78        Notes: (a) the () must be used in the definition even if no parameters
79       are used, (b) the name can be any combination of upper and  lower  case
80       characters  and  numbers, (c) when the macro is used in a command it is
81       prefixed by a & symbol, (d) it is a good idea to always place a %  sym‐
82       bol at the end of the definition, (e) comments (prefixed by a % symbol)
83       can be placed after the macro definition just as in TeX or LaTeX.
84
85        -----examples:
86        %def d2r()_pi_/180%              % degrees2radians
87        %def AreaOfRectangle(x,y)x*y%    % width x, length y
88        %undef d2r()                     % delete the macro
89
90        -----use:
91        var j2= 6*(&d2r(45) + 23)
92        var a3 = 3*&AreaOfRectangle(5,7)
93

GENERAL COMMANDS

95       NUMERICAL EXPRESSIONS
96        When dealing with commands  we  will  refer  frequently  to  the  term
97       `numerical  expression'  by which is meant either (a) a number (integer
98       or decimal), (b) a numeric variable or constant (defined using the  var
99       or  const  command),  (c) any mathsPIC function, macro, or mathematical
100       expression which evaluates to a number, or (d) a pair  of  point  names
101       (e.g. AB) representing the Pythagorean distance between the two points.
102       A leading zero must be used  with decimal fractions less than one.
103
104        In general, if a command's argument accepts a number then it will also
105       accept  a `numerical expression' (<expr>) as defined above. Sometimes a
106       following <unit> is associated with the number or numerical expression,
107       in  which case the number or numerical expression can be delimited by a
108       round bracket (or separated from the unit by a <space>),  as  shown  in
109       the following examples.
110
111        -----examples:
112        ArrowShape(3mm, 20,40)
113        var h=4
114        ArrowShape(h mm, 20, 40)
115        ArrowShape((2*h)mm,20,40)
116
117
118       BACKSLASH \
119        A  leading  backslash  without  a following space indicates that it is
120       part of a PiCTeX, TeX or LaTeX command, in  which case mathsPIC  simply
121       copies  the  whole  line verbatim into the output file. A leading back‐
122       slash followed by one or more spaces makes mathsPIC copy the whole line
123       verbatim into the output file but without the backslash.
124
125
126       USING THE COLOR PACKAGE
127        The standard COLOR package can be used with mathsPIC, but note that it
128       is important to load the COLOR package  after the mathsPIC package.
129
130         It is best to place a comment symbol % at the end of  LaTeX  and  TeX
131       commands to limit white space at the end.
132
133        In  the  event  of  any colour-spill from a diagram into any following
134       text (this used to be a problem in early TeX implementations)  consider
135       using  the  \normalcolor   command as a delimiter within the \beginpic‐
136       ture...\endpicture environment.
137
138       ==============================
139
140       ARROWSHAPE
141        This command defines the shape of an arrowhead, and  allows  different
142       arrowheads to be customised.
143
144       The default arrow shape is equivalent to the Arrowshape(2mm,30,40) com‐
145       mand.  This default arrowhead shape  can  be  reset  using  the  Arrow‐
146       shape(default) command, as shown in the following example.
147
148        -----syntax:
149        arrowshape(<length>[units], <angledeg>, <angledeg>)
150
151        -----examples:
152        Arrowshape(4mm,30,60)
153        drawArrow(AB)
154        Arrowshape(default)
155
156       ==============================
157
158       beginLOOP...endLOOP
159        This is an environment which cycles a block of code a specified number
160       of times.
161
162        -----syntax:
163        beginLoop <expr>
164        ...
165        endLoop
166
167        -----notes:
168        The block of code which lies within the environment  is  input  <expr>
169       times.
170
171        -----example:
172        beginLoop 5
173        ...
174        endLoop
175
176
177       ==============================
178
179       beginSKIP...endSKIP
180        This is an `environment' within which commands are not actioned. It is
181       useful in development for testing isolated commands and excluding other
182       commands.
183
184       ==============================
185
186       CONST
187        The  const  command  is used to define  scalar  constants. Note that a
188       constant-name must begin with a single letter (either  upper  or  lower
189       case),  and  may  have  up to a maximum of three following digits. Note
190       that constants, variables and points have the same name structure,  and
191       a  constant  could  have  the  same  name as a point (and so we suggest
192       points have uppercase letters and variables and constants  have  lower‐
193       case  letters). The scalar argument can be  any numeric expression. New
194       values cannot  be re-allocated  to  existing  constant-names.  If  this
195       occurs mathsPIC will issue an error message.
196
197        -----syntax:
198        const name = <expr>
199
200        -----examples:
201        const r = 20, r4 = r3*tan(0.3)
202
203       ==============================
204
205       DashArray
206        The  dasharray  command  takes an arbitrary number of paired arguments
207       that are used to specify a dash pattern.
208
209        -----syntax
210        dasharray(d1 , g1 , d2 , g2 , ... )
211
212        -----notes
213        The ds denotes the length of a dash and the gs denotes the  length  of
214       the gap between two consecutive dashes. There must be an even number of
215       arguments. If a variable or expression is used then it should be  sepa‐
216       rated  from  the unit either by a <space> or with round brackets ( ) as
217       shown below.
218
219        -----example
220        dasharray(6pt, 2pt, 1pt, 2pt)
221        var d=2
222        dasharray(6pt, 2pt, 1pt, d pt)
223        dasharray(6pt, 2pt, 1pt, (d)pt)
224        dasharray(6pt, 2pt, 1pt, (3*d)pt)
225
226       ==============================
227
228       DrawAngleArc
229        This command draws an arc in the specified angle, a distance  <radius>
230       from  the  angle. The angle is either <internal> (less than 180 deg) or
231       <external> (greater than 180 deg). The direction of the arc  is  either
232       <clockwise> or <anticlockwise>, and this direction must correspond with
233       the letter sequence specified for the angle.   Strange  and  unexpected
234       results will be produced if the four parameters are not internally con‐
235       sistent. The option order angle/radius/internal  or  external/clockwise
236       or anticlockwise is important. The <radius> parameter can be any numer‐
237       ical expression.
238
239        -----syntax:
240        DrawAngleArc{angle(), radius(), external, clockwise}
241
242        -----example:
243        DrawAngleArc{angle(ABC), radius(3), external, clockwise}
244        var r=3
245        DrawAngleArc{angle(ABC), radius(r), external, clockwise}
246
247       ==============================
248
249       DrawAngleArrow
250        This command draws a curved arrow in the specified angle,  a  distance
251       <radius>  from the angle. The angle is either <internal> (less than 180
252       deg) or <external> (greater than 180 deg). The direction of  the  arrow
253       is  either <clockwise> or <anticlockwise>, and this direction must cor‐
254       respond with the letter sequence specified for the angle.  Strange  and
255       unexpected  results  will  be  produced  if the four parameters are not
256       internally consistent. The option order angle/radius/internal/clockwise
257       is important. The <radius> parameter can be any numerical expression.
258
259        -----syntax:
260        DrawAngleArrow{angle(), radius(), external, clockwise}
261
262        -----example:
263        DrawAngleArrow{angle(ABC), radius(3), external, clockwise}
264        var r=3
265        DrawAngleArrow{angle(ABC), radius(r), external, clockwise}
266
267       ==============================
268
269       DrawArrow
270        This  command  draws  an arrow(s) joining two points. The direction of
271       the arrow is in the point order specified.
272
273        -----syntax:
274        drawArrow(<line> [,<line>] ... )
275
276        -----notes:
277        The length option can only refer to one arrow
278
279        -----example:
280        drawArrow(AB)
281        drawArrow(FG, HJ)
282
283       ==============================
284
285       DrawCircle
286        This command draws a circle defined by its radius and  the  point-name
287       of  its  centre.  The  <radius> can be any numerical expression. If the
288       units of the  X  and  Y  axes  are  different,  circles  may  be  drawn
289       strangely,  and  mathsPIC therefore generates a warning message to this
290       effect.
291
292        -----syntax:
293        DrawCircle(<center>, <radius>)
294
295        -----examples:
296        drawCircle(C2,5)
297        drawCircle(C2,r2)
298        drawCircle(C2,r2/tan(1.3))
299        drawCircle(C2,AB)
300
301       ==============================
302
303       DrawCircumcircle
304        This command draws the circumcircle of a triangle.
305
306        -----syntax:
307        DrawCircumcircle(<triangle>)
308
309        -----example:
310        drawCircumcircle(ABC)
311
312       ==============================
313
314       DrawCurve
315        This command draws a smooth quadratic curve through  three  points  in
316       the point order specified. Note that curves drawn using this command do
317       not break to avoid line-free zones associated with the points.
318
319        -----syntax:
320        DrawCurve(<point><point><point>)
321
322        -----example:
323        drawCurve(ABC)
324
325       ==============================
326
327       DrawExcircle
328        This command draws the excircle touching one side of a triangle.
329
330        -----syntax:
331        DrawExcircle(<triangle>, <side>)
332
333        -----example:
334        drawExcircle(ABC, BC)
335
336       ==============================
337
338       DrawIncircle
339        This command draws the incircle of a triangle.
340
341        -----syntax:
342        DrawIncircle(<triangle>)
343
344        -----example:
345        drawIncircle(ABC)
346
347       ==============================
348
349       DrawLine
350        This command draws  a  line  joining  two  or  more  points.  Use  the
351       Linethickness  command  to vary thickness. This command uses the PiCTeX
352       \putrule command for horizontal and vertical lines, and the \plot  com‐
353       mand for all other orientations.
354
355        -----syntax:
356        DrawLine( <points> [, <points>] )
357
358        -----notes:
359        <points> is any sequence of two or more point names.
360        <expr> is any numerical expression.
361        Lines are drawn in the order specified.
362        Lines are separated by a comma.
363
364        -----examples:
365        drawline(AB)
366        drawline(BCDE)
367        drawline(FG, HJK, PQRST)
368
369       ==============================
370
371       DrawPerpendicular
372        This command draws the perpendicular from a point to a line.
373
374        -----syntax:
375        DrawPerpendicular(<point>, <line)
376
377        -----example:
378        drawPerpendicular(P,AB)
379
380       ==============================
381
382       DrawPoint
383        This  command  draws  the  point-symbol at the  point-location. Commas
384       must not be used to separate point names. The default  point-symbol  is
385       bullet  unless  an  optional  point-symbol (or string of characters) is
386       specified in the associated point command.
387
388        -----syntax:
389        DrawPoint(<point> [<point> ..])
390
391        -----examples:
392        drawpoint(T4)
393        drawpoint(ABCDEF)
394        drawpoint(P1 P2 P3 P4)
395
396       ==============================
397
398       DrawRightangle
399        This command draws the standard right-angle  symbol  in  the  internal
400       angle specified at the size specified by <expr>.
401
402        -----syntax:
403        DrawRightangle(<angle>, <expr>)
404
405        -----notes:
406        The <expr> can be any numerical expression.
407
408        -----example:
409        drawRightangle(ABC,3)
410        drawRightangle(ABC,PQ)
411        var d=5
412        drawRightangle(ABC,d)
413
414       ==============================
415
416       DrawSquare
417        This  command draws a square defined by its side and the point-name of
418       its centre. The <sidelength> can be any numerical expression.
419
420        -----syntax:
421        DrawSquare(<centerpoint>, <sidelength>)
422
423        -----examples:
424        drawSquare(P,5)
425        var s2=3, j=2
426        drawSquare(P,s2)
427        drawSquare(P, s2*4/(3*j))
428        drawSquare(P,AB)
429
430       ==============================
431
432       DrawThickArrow
433        This command draws a thick arrow(s) joining two points. The  direction
434       of  the  arrow is in the point order specified. The shape of the arrow‐
435       head is controlled by the ArrowShape command.
436
437        -----syntax:
438        drawThickArrow(<line> [,<line>,...])
439
440        -----examples:
441        drawThickarrow(BC)
442        drawThickarrow(PQ, RS)
443
444       ==============================
445
446       DrawThickLine
447        This command draws a thick line(s) joining two points.  The  direction
448       of the line is in the point order specified. Use the Linethickness com‐
449       mand to vary thickness of a line.
450
451        -----syntax:
452        drawThickLine(<line> [,<line>,...])
453
454        -----examples:
455        drawThickline(BC)
456        drawThickline(PQ, RS)
457
458       ==============================
459
460       InputFile
461        This command inputs a plain text file  containing  mathsPIC  commands.
462       Optionally,  the  file  can  be input several times, in which case this
463       command functions like a DO--LOOP.  The <loopnumber> can be any numeri‐
464       cal  expression.  If  the  <loopnumber> is not an integer then mathsPIC
465       will round the value down to the nearest integer. See also  the  begin‐
466       LOOP ... endLOOP commands.
467
468        -----syntax:
469        inputFile[*](<filename>)[<loopnumber>]
470
471        -----notes:
472        The  inputfile*  command  is  used to input a file in verbatim, i.e. a
473       file with no mathsPIC commands, for example,  a  file  containing  only
474       PiCTeX  commands  or data-points for plotting etc. Note that the input‐
475       file* command  has  no  <loopnumber>  option.  Note  also  that  PiCTeX
476       requires a ODD number of points.
477
478        -----examples:
479        inputFile(myfile.dat)[4]
480        inputFile*(mycurvedata.dat)
481
482       ==============================
483
484       LineThickness
485        This  command  sets a particular linethickness. The command linethick‐
486       ness(default) restores the working linethickness to the  default  value
487       of  0.4pt.   The  current value of the linethickness (in current units)
488       can be accessed using the var command (this can be useful when  drawing
489       figures using thick lines) .
490
491        -----syntax:
492        LineThickness(<expr><units>)
493        LineThickness(default)
494        var t = _linethickness_
495
496        -----notes:
497        This  command  also  sets  the font to cmr and plotsymbol to \CM . and
498       also sets the rule thickness for drawing horizontal and vertical lines.
499       It  is  important to include a leading zero with decimal fractions less
500       than one.
501
502        -----examples:
503        linethickness(2pt)
504        var t=3
505        linethickness((t)pt)
506        lineThickness((2*t)pt)
507        linethickness(default)
508        var t = _linethickness_
509
510        -----caution:
511        Note that there is a similar PiCTeX  command  with the same name  (but
512       with a different syntax).
513
514       ==============================
515
516       PAPER
517        Defines  the  plotting area in terms of the options units(), xrange(),
518       yrange(), axes(), and ticks(). The  units()  argument  must  contain  a
519       numeric  value  and  a  valid  TeX  length  unit  mm, cm, pt, pc(pica),
520       in(inch), bp(big point), dd(didot), cc(cicero), sp(scaled point). The X
521       and  Y  axes  can  have different units (see second example below). The
522       axes() arguments XYTBLR refer to the X and Y axes, and  the  Top,  Bot‐
523       tom,  Left and Right axes. A * following one of the axes disables ticks
524       on that axis. The X and Y axes pass through the zeros.
525
526        -----examples:
527        paper{units(1cm),xrange(0,10),yrange(0,10)}
528        paper{units(2cm,1cm),xrange(0,10),yrange(0,10),axes(LB)}
529        paper{units(1mm),xrange(0,100),yrange(0,100),axes(XY)}
530        paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRTBXY),ticks(1,1)}
531        paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRT*B*)}
532
533       ==============================
534
535       POINT
536        Defines a new point by allocating coordinates to a new point name. The
537       * option re-allocates coordinates to an existing point name.
538
539        -----syntax:
540        POINT[*](<name>){<point>}[symbol=<chars>, radius=<expr>]
541        POINT[*](<name>){<location>}[symbol=<chars>, radius=<expr>]
542
543        -----notes:
544        <name> one leading letter plus maximum of three trailing digits
545        <chars> any TeX string allowed in an \hbox{}
546        <expr> any numerical expression
547        The polar(r,theta) option  defaults to radians for the angle theta. To
548       work in degrees then must append <deg> eg: polar(r,theta deg). Can  use
549       <direction()> and <directiondeg()> to replace theta. Note that the term
550       vector(AB) means use same (r, theta) as AB.
551
552        -----examples:
553        point(A){5,5}
554        point(B2){22,46}[symbol=$\odot$]
555        point(B2){22,46}[symbol=circle(2),radius=5]
556        var r=3
557        point(B2){22,46}[symbol=square(3),radius=r]
558        point(B123){22,46}[radius=5]
559        point(D2){B2, shift(5,5)}
560        var s = 3
561        point(D2){B2, shift(2*s,4*s)}
562        point(D3){D2, polar(6,32 deg)}
563        point(D4){D2, polar(6,1.2 rad)}
564        point(D4){D2, polar(6, direction(AB))}      %% radians by default
565        point(D4){D2, polar(6, directiondeg(AB) deg)}
566        point(G2){Q, rotate(P, 23 deg)}
567        point(G2){Q, vector(AB)}
568        point(D2){intersection(AB,CD)}
569        point(F){PointOnLine(AB,5.3)}
570        point(G){perpendicular(P,AB)}
571        point(H){circumcircleCenter(ABC)}
572        point(J){incircleCenter(ABC)}
573        point(K){excircleCenter(ABC,BC)}
574        point*(A){6,3}
575        point*(P){Q}
576        point*(B){B, shift(5,0)}
577        point*(P){xcoord(J),ycoord(K)}
578
579       ==============================
580
581       PointSymbol
582        This command allows the default point-symbol \bullet (with zero  line-
583       free  radius)  to  be  changed. The PointSymbol command is particularly
584       useful where a set of points uses the same point-symbol,  for  example,
585       when drawing graphs. The point-symbol can be reset to the default \bul‐
586       let  using the command PointSymbol(default).
587
588        -----syntax:
589        PointSymbol(<symbol>, <line-free-radius>)
590        PointSymbol(default)
591
592        -----notes:
593        The PointSymbol command only influences subsequent point commands.
594        The optional  square  bracket  of  the  point  command  overrides  the
595       PointSymbol command.
596
597        -----examples:
598        PointSymbol($\odot$, 0.7)
599        PointSymbol(default)
600
601       ==============================
602
603       SYSTEM
604        This  command  allows  the user to access the command line and execute
605       standard Linux commands. A important use for this command is to  run  a
606       Perl program.
607
608        -----syntax:
609        System("<command>")
610
611        -----notes:
612        The <command> string must be in inverted commas.
613
614        -----example:
615        system("dir > mydir-listing.txt")
616        system("perl myperlprogram.pl")
617
618       ==============================
619
620       SHOW....
621        This command makes mathsPIC return the value of a calculation or spec‐
622       ified parameter; for example, the value of a particular angle,  or  the
623       length of a line. The result is shown in the output-file as a commented
624       line. This allows mathsPIC commands to be  adjusted  in  the  light  of
625       calculations. There are currently five such commands as follows.
626
627        -----syntax:
628        showLength(AB)
629        showAngle(ABC)       % returns angle in radians
630        showAngledeg(ABC)    % returns angle in degrees
631        showArea(ABC)
632        showPoints
633        showVariables
634
635       ==============================
636
637       TEXT
638        This  command  places a text-string at a specific location. By default
639       the text is centered  vertically  and  horizontally  at  the  specified
640       point.  Optionally, text can be placed relative to a point using appro‐
641       priate combinations of the PiCTeX  `position' options l  t  r  B  b  to
642       align  the  (l)eft edge, (r)ight edge, (t)op edge, (B)aseline, (b)ottom
643       edge respectively of the text box with the point-location.
644
645        Remember that the default units for the angle argument of the  polar()
646       expression  is radians; hence you MUST append `deg' if you want to work
647       in degrees
648
649        -----syntax:
650        text(<string>){<location>}[<position options>]
651        text(<string>){<pointname>, shift(<x>,<y>)}[]
652        text(<string>){<pointname>, polar(<r>,<angle>[rad])}[]
653
654        -----examples:
655        text(A){5,6}
656        text($A_1$){A1, shift(2, 2)}
657        text(Z2){Z2, shift(5, -5)}[tr]
658        text(Z3){Z2, polar(5, 20 deg)}[Br]
659        text(Z4){Z2, polar(5, 1.34 rad)}
660        text(\framebox{Z5}){Z5}
661
662       ==============================
663
664       VAR
665        The var command is used to define scalar  variables.  It  can  be  any
666       numerical  expression.  A variable-name must begin with a single letter
667       (either upper or lower case), and may have up to a maximum of four fol‐
668       lowing  digits.  If  a  more detailed variable name is required, then a
669       simple alternative is to use a mathsPIC macro---as any  string  can  be
670       allocated  via macros (see the beginning of this chapter for details on
671       macros).
672
673         Note that variables, constants and points have the same  name  struc‐
674       ture,  and a variable can have the same name as a point (and so we sug‐
675       gest points have uppercase letters and  variables  and  constants  have
676       lowercase  letters).  New  values can be re-allocated to existing vari‐
677       able-names; however, when this occurs then mathsPIC does  not  issue  a
678       warning message to hightlight this fact.
679
680        If  it  is  important to be warned if a potential variable is acciden‐
681       tally reallocated then one should  consider  using  the  const  command
682       instead (since mathsPIC does generate an error message if a constant is
683       reallocated).
684
685        -----syntax:
686        var  <name> = <expr>
687
688        -----notes:
689        In addition to the mathematical functions mathsPIC functions which can
690       be used with the var command are:
691
692        angle(<three-points>)          % returns angle in radians
693        angledeg(<three-points>)       % returns angle in degrees
694        area(<three-points>)
695        xcoord(<point>)
696        ycoord(<point>)
697        direction(<two-points>)     % returns angular direction in radians
698        directiondeg(<two-points>)  % returns angular direction in degrees
699
700        -----examples:
701        var r = 20, r4 = r3*tan(0.3), j = (r*2e3)**2,  r5 = AB
702        var e = _e_, p1 = _Pi_
703        var t = _linethickness_  % returns linethickness in current units
704        var g137 = angle(ABC)    %(default: returns in radians)
705        var g = angledeg(ABC)    % angle in degrees
706        var h = area(ABC)
707        var x2 = xcoord(A), y2 = ycoord(A)
708        var m5 = 12 rem 3     % remainder after dividing by 3
709        var r1 = direction(PQ)   % in radians
710        var d1 = directiondeg(PQ)
711
712       ==============================
713

SEE ALSO

715       The mathsPIC package manual and examples
716

BUGS

718       Please  report  bugs to Dick Nickalls (dick [AT] nickalls [dot] org) or
719       to Apostolos Syropoulos
720
721
722
723
724mathsPIC perl version           April 26, 2010                     mathsPIC(1)
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