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#### NAME

       mathsPIC



#### AUTHORS

       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

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) regular 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 fractions 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-LINEUSE

       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

-o defines the output file name



#### MACROCOMMANDS

       macro  definition  commands  are  prefixed  with  %def  and can take  either 0, 1, or more
parameters. Macros will generally be used as part of a var command as shown below.  Macros
are deleted using the %undef command.

-----syntax:
%def MACRONAME(parameters)<macrodefinition>
%undef MACRONAME(parameters)

-----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 % symbol 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 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)



#### GENERALCOMMANDS

       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 backslash 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.

In  the event of any colour-spill from a diagram into any following text (this used to be
a problem in early TeX implementations) consider using  the  \normalcolor   command  as  a
delimiter within the \beginpicture...\endpicture environment.

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

ARROWSHAPE
This  command  defines  the  shape of an arrowhead, and allows different arrowheads to be
customised.

The default arrow shape is equivalent to the Arrowshape(2mm,30,40) command.  This  default
arrowhead  shape  can  be  reset  using  the  Arrowshape(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 lowercase 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>

-----examples:
const r = 20, r4 = r3*tan(0.3)

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

DashArray
The  dasharray  command  takes  an  arbitrary number of paired arguments that are used to
specify a dash pattern.

-----syntax
dasharray(d1 , g1 , d2 , g2 , ... )

-----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 separated 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 consistent. The option
order angle/radius/internal or  external/clockwise  or  anticlockwise  is  important.  The
<radius> parameter can be any numerical expression.

-----syntax:

-----example:
var r=3

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

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 correspond with the letter sequence specified for the angle.   Strange  and
unexpected  results will be produced if the four parameters are not internally consistent.
be any numerical expression.

-----syntax:

-----example:
var r=3

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

DrawArrow
This  command  draws an arrow(s) joining two points. The direction of the arrow is in the
point order specified.

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

-----notes:
The length option can only refer to one arrow

-----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:

-----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:
drawExcircle(ABC, BC)

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

DrawIncircle
This command draws the incircle of a triangle.

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

-----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 command 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
This command draws the standard right-angle symbol in the internal angle specified at the
size specified by <expr>.

-----syntax:
DrawRightangle(<angle>, <expr>)

-----notes:
The <expr> can be any numerical expression.

-----example:
drawRightangle(ABC,3)
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 arrowhead  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 command 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 numerical expression. If the <loopnumber> is not an  integer  then
mathsPIC  will  round  the  value  down to the nearest integer. See also the beginLOOP ...
endLOOP commands.

-----syntax:
inputFile[*](<filename>)[<loopnumber>]

-----notes:
The inputfile* command is used to input a file in verbatim, i.e. a file with no  mathsPIC
commands,  for example, a file containing only PiCTeX commands or data-points for plotting
etc. Note that the inputfile* command has no <loopnumber> option. Note  also  that  PiCTeX
requires a ODD number of points.

-----examples:
inputFile(myfile.dat)[4]
inputFile*(mycurvedata.dat)

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

LineThickness
This command sets a particular linethickness. The command linethickness(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, Bottom, 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)}
paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRTBXY),ticks(1,1)}
paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRT*B*)}

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

POINT
Defines a new point by allocating coordinates to a new  point  name.  The  *  option  re-
allocates coordinates to an existing point name.

-----syntax:

-----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=$\odot$]
var r=3
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, 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 \bullet  using the command PointSymbol(default).

-----syntax:
PointSymbol(default)

-----notes:
The PointSymbol command only influences subsequent point commands.
The optional square bracket of the point command overrides the PointSymbol command.

-----examples:
PointSymbol($\odot$, 0.7)
PointSymbol(default)

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

SYSTEM
This command allows the user to access  the  command  line  and  execute  standard  Linux
commands. A important use for this command is to run a Perl program.

-----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 specified 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 appropriate 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>)}[]

-----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(\framebox{Z5}){Z5}

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

VAR
The var command is used to define scalar variables. It can be any numerical expression. A
variable-name must begin with a single letter (either upper or lower case), and  may  have
up  to  a  maximum of four following digits. If a more detailed variable name is required,
then a simple alternative is to use a mathsPIC macro---as any string can be allocated  via
macros (see the beginning of this chapter for details on macros).

Note  that  variables, constants and points have the same name structure, and a variable
can have the same name as a point (and so we suggest points  have  uppercase  letters  and
variables  and  constants  have  lowercase  letters).  New  values  can be re-allocated to
existing variable-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 accidentally 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)

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



#### SEEALSO

       The mathsPIC package manual and examples



#### BUGS

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