# mathspic

       A. Syropoulos and R.W.D. Nickalls (April 26, 2010)

asyropoulos[at]<yahoo><com>
dick[at]<nickalls><org>

DESCRIPTION
mathsPIC  is  a  Perl  filter  program for PiCTeX. mathsPIC has its own
macro and macro library capability, and allows use of mathsPIC, PiCTeX,
TeX  and  LaTeX  commands. A significant feature of mathsPIC is that it
allows access to the command-line, and so allows  the  user  to  extend
mathsPIC commands by calling Perl and other programs written to perform
particular drawing actions. See the package manual for full details and
examples. The latest version can be downloaded from

CTAN: tex-archive/graphics/pictex/mathspic/perl

Commands  which  can be used in the mathsPIC script file fall into four
main groups (a) mathsPIC macro commands (prefixed with %def), (b) regu-
lar  mathsPIC  commands  (do  not have a backslash), (c) regular PiCTeX
commands (all have a backslash), and (d) regular TeX and LaTeX commands
(all have a backslash).

The  following  mathematics functions can used (note that decimal frac-
tions having an absolute value less than 1 must have a  leading  zero).
Note also that all the trignometric functions require their argument in
radians.

Trigonometric: sin(), cos(), tan(), asin(), acos(), atan()

Remainder: rem(); eg var  r=12 rem(5)

Integer: int(); eg var  r= int(3.87) --> 3

Sign (returns -1, 0, +1): sgn(); eg var  s=sgn(-3.27) --> -1

Square root: sqrt(); eg var s = sqrt(14)

Exponentiation: **; eg var j = r**2

Pi constant (3.14159...):  _Pi_  and  _pi_

e constant (2.71828...):  _E_  and  _e_

Linethickness:  _linethickness_  ; eg  var t = _linethickness_

COMMAND-LINE USE
perl mathspic.pl [-b] [-c] [-h] [-o  <outfile>]  <infile>

-b enables beep if mathsPIC detects an error

-c disables the writing of comments to output file

-h displays the help file

-----notes:
Notes: (a) the () must be used in the definition even if no parameters
are used, (b) the name can be any combination of upper and  lower  case
characters  and  numbers, (c) when the macro is used in a command it is
prefixed by a & symbol, (d) it is a good idea to always place a %  sym-
bol at the end of the definition, (e) comments (prefixed by a % symbol)
can be placed after the macro definition just as in TeX or LaTeX.

-----examples:
%def d2r()_pi_/180%              % degrees2radians
%def AreaOfRectangle(x,y)x*y%    % width x, length y
%undef d2r()                     % delete the macro

-----use:
var j2= 6*(&d2r(45) + 23)
var a3 = 3*&AreaOfRectangle(5,7)

GENERAL COMMANDS
NUMERICAL EXPRESSIONS
When dealing with commands  we  will  refer  frequently  to  the  term
numerical  expression'  by which is meant either (a) a number (integer
or decimal), (b) a numeric variable or constant (defined using the  var
or  const  command),  (c) any mathsPIC function, macro, or mathematical
expression which evaluates to a number, or (d) a pair  of  point  names
(e.g. AB) representing the Pythagorean distance between the two points.
A leading zero must be used  with decimal fractions less than one.

In general, if a command's argument accepts a number then it will also
accept  a numerical expression' (<expr>) as defined above. Sometimes a
following <unit> is associated with the number or numerical expression,
in  which case the number or numerical expression can be delimited by a
round bracket (or separated from the unit by a <space>),  as  shown  in
the following examples.

-----examples:
ArrowShape(3mm, 20,40)
var h=4
ArrowShape(h mm, 20, 40)
ArrowShape((2*h)mm,20,40)

BACKSLASH \
A  leading  backslash  without  a following space indicates that it is
part of a PiCTeX, TeX or LaTeX command, in  which case mathsPIC  simply
copies  the  whole  line verbatim into the output file. A leading back-
slash followed by one or more spaces makes mathsPIC copy the whole line
verbatim into the output file but without the backslash.

USING THE COLOR PACKAGE
The standard COLOR package can be used with mathsPIC, but note that it
is important to load the COLOR package  after the mathsPIC package.

It is best to place a comment symbol % at the end of  LaTeX  and  TeX
commands to limit white space at the end.

mand.  This default arrowhead shape  can  be  reset  using  the  Arrow-
shape(default) command, as shown in the following example.

-----syntax:
arrowshape(<length>[units], <angledeg>, <angledeg>)

-----examples:
Arrowshape(4mm,30,60)
drawArrow(AB)
Arrowshape(default)

==============================

beginLOOP...endLOOP
This is an environment which cycles a block of code a specified number
of times.

-----syntax:
beginLoop <expr>
...
endLoop

-----notes:
The block of code which lies within the environment  is  input  <expr>
times.

-----example:
beginLoop 5
...
endLoop

==============================

beginSKIP...endSKIP
This is an environment' within which commands are not actioned. It is
useful in development for testing isolated commands and excluding other
commands.

==============================

CONST
The  const  command  is used to define  scalar  constants. Note that a
constant-name must begin with a single letter (either  upper  or  lower
case),  and  may  have  up to a maximum of three following digits. Note
that constants, variables and points have the same name structure,  and
a  constant  could  have  the  same  name as a point (and so we suggest
points have uppercase letters and variables and constants  have  lower-
case  letters). The scalar argument can be  any numeric expression. New
values cannot  be re-allocated  to  existing  constant-names.  If  this
occurs mathsPIC will issue an error message.

-----syntax:
const name = <expr>

-----notes
The ds denotes the length of a dash and the gs denotes the  length  of
the gap between two consecutive dashes. There must be an even number of
arguments. If a variable or expression is used then it should be  sepa-
rated  from  the unit either by a <space> or with round brackets ( ) as
shown below.

-----example
dasharray(6pt, 2pt, 1pt, 2pt)
var d=2
dasharray(6pt, 2pt, 1pt, d pt)
dasharray(6pt, 2pt, 1pt, (d)pt)
dasharray(6pt, 2pt, 1pt, (3*d)pt)

==============================

DrawAngleArc
This command draws an arc in the specified angle, a distance  <radius>
from  the  angle. The angle is either <internal> (less than 180 deg) or
<external> (greater than 180 deg). The direction of the arc  is  either
<clockwise> or <anticlockwise>, and this direction must correspond with
the letter sequence specified for the angle.   Strange  and  unexpected
results will be produced if the four parameters are not internally con-
sistent. The option order angle/radius/internal  or  external/clockwise
or anticlockwise is important. The <radius> parameter can be any numer-
ical expression.

-----syntax:
DrawAngleArc{angle(), radius(), external, clockwise}

-----example:
DrawAngleArc{angle(ABC), radius(3), external, clockwise}
var r=3
DrawAngleArc{angle(ABC), radius(r), external, clockwise}

==============================

DrawAngleArrow
This command draws a curved arrow in the specified angle,  a  distance
<radius>  from the angle. The angle is either <internal> (less than 180
deg) or <external> (greater than 180 deg). The direction of  the  arrow
is  either <clockwise> or <anticlockwise>, and this direction must cor-
respond with the letter sequence specified for the angle.  Strange  and
unexpected  results  will  be  produced  if the four parameters are not
internally consistent. The option order angle/radius/internal/clockwise
is important. The <radius> parameter can be any numerical expression.

-----syntax:
DrawAngleArrow{angle(), radius(), external, clockwise}

-----example:
DrawAngleArrow{angle(ABC), radius(3), external, clockwise}
var r=3
DrawAngleArrow{angle(ABC), radius(r), external, clockwise}

-----example:
drawArrow(AB)
drawArrow(FG, HJ)

==============================

DrawCircle
This command draws a circle defined by its radius and  the  point-name
of  its  centre.  The  <radius> can be any numerical expression. If the
units of the  X  and  Y  axes  are  different,  circles  may  be  drawn
strangely,  and  mathsPIC therefore generates a warning message to this
effect.

-----syntax:
DrawCircle(<center>, <radius>)

-----examples:
drawCircle(C2,5)
drawCircle(C2,r2)
drawCircle(C2,r2/tan(1.3))
drawCircle(C2,AB)

==============================

DrawCircumcircle
This command draws the circumcircle of a triangle.

-----syntax:
DrawCircumcircle(<triangle>)

-----example:
drawCircumcircle(ABC)

==============================

DrawCurve
This command draws a smooth quadratic curve through  three  points  in
the point order specified. Note that curves drawn using this command do
not break to avoid line-free zones associated with the points.

-----syntax:
DrawCurve(<point><point><point>)

-----example:
drawCurve(ABC)

==============================

DrawExcircle
This command draws the excircle touching one side of a triangle.

-----syntax:
DrawExcircle(<triangle>, <side>)
-----example:
drawIncircle(ABC)

==============================

DrawLine
This command draws  a  line  joining  two  or  more  points.  Use  the
Linethickness  command  to vary thickness. This command uses the PiCTeX
\putrule command for horizontal and vertical lines, and the \plot  com-
mand for all other orientations.

-----syntax:
DrawLine( <points> [, <points>] )

-----notes:
<points> is any sequence of two or more point names.
<expr> is any numerical expression.
Lines are drawn in the order specified.
Lines are separated by a comma.

-----examples:
drawline(AB)
drawline(BCDE)
drawline(FG, HJK, PQRST)

==============================

DrawPerpendicular
This command draws the perpendicular from a point to a line.

-----syntax:
DrawPerpendicular(<point>, <line)

-----example:
drawPerpendicular(P,AB)

==============================

DrawPoint
This  command  draws  the  point-symbol at the  point-location. Commas
must not be used to separate point names. The default  point-symbol  is
bullet  unless  an  optional  point-symbol (or string of characters) is
specified in the associated point command.

-----syntax:
DrawPoint(<point> [<point> ..])

-----examples:
drawpoint(T4)
drawpoint(ABCDEF)
drawpoint(P1 P2 P3 P4)

==============================

drawRightangle(ABC,PQ)
var d=5
drawRightangle(ABC,d)

==============================

DrawSquare
This  command draws a square defined by its side and the point-name of
its centre. The <sidelength> can be any numerical expression.

-----syntax:
DrawSquare(<centerpoint>, <sidelength>)

-----examples:
drawSquare(P,5)
var s2=3, j=2
drawSquare(P,s2)
drawSquare(P, s2*4/(3*j))
drawSquare(P,AB)

==============================

DrawThickArrow
This command draws a thick arrow(s) joining two points. The  direction
of  the  arrow is in the point order specified. The shape of the arrow-
head is controlled by the ArrowShape command.

-----syntax:
drawThickArrow(<line> [,<line>,...])

-----examples:
drawThickarrow(BC)
drawThickarrow(PQ, RS)

==============================

DrawThickLine
This command draws a thick line(s) joining two points.  The  direction
of the line is in the point order specified. Use the Linethickness com-
mand to vary thickness of a line.

-----syntax:
drawThickLine(<line> [,<line>,...])

-----examples:
drawThickline(BC)
drawThickline(PQ, RS)

==============================

InputFile
This command inputs a plain text file  containing  mathsPIC  commands.
Optionally,  the  file  can  be input several times, in which case this
command functions like a DO--LOOP.  The <loopnumber> can be any numeri-
requires a ODD number of points.

-----examples:
inputFile(myfile.dat)
inputFile*(mycurvedata.dat)

==============================

LineThickness
This  command  sets a particular linethickness. The command linethick-
ness(default) restores the working linethickness to the  default  value
of  0.4pt.   The  current value of the linethickness (in current units)
can be accessed using the var command (this can be useful when  drawing
figures using thick lines) .

-----syntax:
LineThickness(<expr><units>)
LineThickness(default)
var t = _linethickness_

-----notes:
This  command  also  sets  the font to cmr and plotsymbol to \CM . and
also sets the rule thickness for drawing horizontal and vertical lines.
It  is  important to include a leading zero with decimal fractions less
than one.

-----examples:
linethickness(2pt)
var t=3
linethickness((t)pt)
lineThickness((2*t)pt)
linethickness(default)
var t = _linethickness_

-----caution:
Note that there is a similar PiCTeX  command  with the same name  (but
with a different syntax).

==============================

PAPER
Defines  the  plotting area in terms of the options units(), xrange(),
yrange(), axes(), and ticks(). The  units()  argument  must  contain  a
numeric  value  and  a  valid  TeX  length  unit  mm, cm, pt, pc(pica),
in(inch), bp(big point), dd(didot), cc(cicero), sp(scaled point). The X
and  Y  axes  can  have different units (see second example below). The
axes() arguments XYTBLR refer to the X and Y axes, and  the  Top,  Bot-
tom,  Left and Right axes. A * following one of the axes disables ticks
on that axis. The X and Y axes pass through the zeros.

-----examples:
paper{units(1cm),xrange(0,10),yrange(0,10)}
paper{units(2cm,1cm),xrange(0,10),yrange(0,10),axes(LB)}
paper{units(1mm),xrange(0,100),yrange(0,100),axes(XY)}

-----notes:
<name> one leading letter plus maximum of three trailing digits
<chars> any TeX string allowed in an \hbox{}
<expr> any numerical expression
The polar(r,theta) option  defaults to radians for the angle theta. To
work in degrees then must append <deg> eg: polar(r,theta deg). Can  use
<direction()> and <directiondeg()> to replace theta. Note that the term
vector(AB) means use same (r, theta) as AB.

-----examples:
point(A){5,5}
point(B2){22,46}[symbol=$\odot$]
point(B2){22,46}[symbol=circle(2),radius=5]
var r=3
point(B2){22,46}[symbol=square(3),radius=r]
point(B123){22,46}[radius=5]
point(D2){B2, shift(5,5)}
var s = 3
point(D2){B2, shift(2*s,4*s)}
point(D3){D2, polar(6,32 deg)}
point(D4){D2, polar(6,1.2 rad)}
point(D4){D2, polar(6, direction(AB))}      %% radians by default
point(D4){D2, polar(6, directiondeg(AB) deg)}
point(G2){Q, rotate(P, 23 deg)}
point(G2){Q, vector(AB)}
point(D2){intersection(AB,CD)}
point(F){PointOnLine(AB,5.3)}
point(G){perpendicular(P,AB)}
point(H){circumcircleCenter(ABC)}
point(J){incircleCenter(ABC)}
point(K){excircleCenter(ABC,BC)}
point*(A){6,3}
point*(P){Q}
point*(B){B, shift(5,0)}
point*(P){xcoord(J),ycoord(K)}

==============================

PointSymbol
This command allows the default point-symbol \bullet (with zero  line-
free  radius)  to  be  changed. The PointSymbol command is particularly
useful where a set of points uses the same point-symbol,  for  example,
when drawing graphs. The point-symbol can be reset to the default \bul-
let  using the command PointSymbol(default).

-----syntax:
PointSymbol(<symbol>, <line-free-radius>)
PointSymbol(default)

-----notes:
The PointSymbol command only influences subsequent point commands.
The optional  square  bracket  of  the  point  command  overrides  the
PointSymbol command.
-----syntax:
System("<command>")

-----notes:
The <command> string must be in inverted commas.

-----example:
system("dir > mydir-listing.txt")
system("perl myperlprogram.pl")

==============================

SHOW....
This command makes mathsPIC return the value of a calculation or spec-
ified parameter; for example, the value of a particular angle,  or  the
length of a line. The result is shown in the output-file as a commented
line. This allows mathsPIC commands to be  adjusted  in  the  light  of
calculations. There are currently five such commands as follows.

-----syntax:
showLength(AB)
showAngle(ABC)       % returns angle in radians
showAngledeg(ABC)    % returns angle in degrees
showArea(ABC)
showPoints
showVariables

==============================

TEXT
This  command  places a text-string at a specific location. By default
the text is centered  vertically  and  horizontally  at  the  specified
point.  Optionally, text can be placed relative to a point using appro-
priate combinations of the PiCTeX  position' options l  t  r  B  b  to
align  the  (l)eft edge, (r)ight edge, (t)op edge, (B)aseline, (b)ottom
edge respectively of the text box with the point-location.

Remember that the default units for the angle argument of the  polar()
expression  is radians; hence you MUST append deg' if you want to work
in degrees

-----syntax:
text(<string>){<location>}[<position options>]
text(<string>){<pointname>, shift(<x>,<y>)}[]
text(<string>){<pointname>, polar(<r>,<angle>[rad])}[]

-----examples:
text(A){5,6}
text($A_1$){A1, shift(2, 2)}
text(Z2){Z2, shift(5, -5)}[tr]
text(Z3){Z2, polar(5, 20 deg)}[Br]
text(Z4){Z2, polar(5, 1.34 rad)}
text(\framebox{Z5}){Z5}

ture,  and a variable can have the same name as a point (and so we sug-
gest points have uppercase letters and  variables  and  constants  have
lowercase  letters).  New  values can be re-allocated to existing vari-
able-names; however, when this occurs then mathsPIC does  not  issue  a
warning message to hightlight this fact.

If  it  is  important to be warned if a potential variable is acciden-
tally reallocated then one should  consider  using  the  const  command
instead (since mathsPIC does generate an error message if a constant is
reallocated).

-----syntax:
var  <name> = <expr>

-----notes:
In addition to the mathematical functions mathsPIC functions which can
be used with the var command are:

angle(<three-points>)          % returns angle in radians
angledeg(<three-points>)       % returns angle in degrees
area(<three-points>)
xcoord(<point>)
ycoord(<point>)
direction(<two-points>)     % returns angular direction in radians
directiondeg(<two-points>)  % returns angular direction in degrees

-----examples:
var r = 20, r4 = r3*tan(0.3), j = (r*2e3)**2,  r5 = AB
var e = _e_, p1 = _Pi_
var t = _linethickness_  % returns linethickness in current units
var g137 = angle(ABC)    %(default: returns in radians)
var g = angledeg(ABC)    % angle in degrees
var h = area(ABC)
var x2 = xcoord(A), y2 = ycoord(A)
var m5 = 12 rem 3     % remainder after dividing by 3
var r1 = direction(PQ)   % in radians
var d1 = directiondeg(PQ)

==============================

SEE ALSO
The mathsPIC package manual and examples

BUGS
Please  report  bugs to Dick Nickalls (dick [AT] nickalls [dot] org) or
to Apostolos Syropoulos

mathsPIC perl version           April 26, 2010                     mathsPIC(1)`