The code that produced this output is listed below. The additions to the basic graph paper are in bold.
Here is an example of filling a region
in polar coordinates.
The code that produced this output is listed below.
The additions to the basic graph paper are in bold.
%!PS-Adobe-3.0 EPSF-3.0
%%Title: Blank Graph
%%Creator:Laurence R. Taylor taylor.2@nd.edu www.nd.edu/~taylor
%%Copyright (C) 2000
%%Distribute freely but modifications may remain private
%%CreationDate: ??
%%Version: 1.0.0
%%Data is set near the end of this file. (Search for data.)
%%EXCEPT that you may need to adjust the BoundingBox
%%BoundingBox: -100 -100 100 100
save
%%Initialize variables
/arrx 0 def
/varx 0 def
/ReqFun{}def
/ThetaeqFun{}def
/XeqFun{}def
/YeqFun{}def
/fun_v {}def
/fun_a {}def
/fun_b {}def
/start_v 0 def
/inc_v 0 def
/end_v 0 def
/mX 0 def
/pX 0 def
/mY 0 def
/pY 0 def
/xTick 0 def
/yTick 0 def
/tickSize{3}def
/sxn 0 def
%%TEX fonts
/fontscale{8}def
/vfont{fontscale}def %% vertical distance from bottom of tick to baseline of labels
/hfont{fontscale 2 div}def %% horizontal distance from tick to right edge of labels
/CMR{
/CMR10 findfont fontscale scalefont setfont
}def
/CMMI{
/CMMI10 findfont fontscale scalefont setfont
}def
/poly{
%% Computes a polynomial
%% /YeqFun{ [a_n ... a_1 a_0] poly}def
%% If followed by graph graphs the polynomial
%% y=a_nx^n+ ... +a_1x+a_0
/arrx exch def
/varx exch def
0 0 1 arrx length 1 sub
{arrx exch get exch varx mul add}for
} def
/ADD{
%% USAGE: number {function1}{function2} ADD
%% pops the arguments and pushes function1(number)+function2(number)
/fun_a exch def
/fun_b exch def
dup fun_b exch fun_a add
}def
/MUL{
%% USAGE: number {function1}{function2} MUL
%% pops the arguments and pushes function1(number)*function2(number)
/fun_a exch def
/fun_b exch def
dup fun_b exch fun_a mul
}def
/DIV{
%% USAGE: number {function1}{function2} DIV
%% pops the arguments and pushes function1(number)/function2(number)
%% after checking function2(number) ne 0
/fun_a exch def
/fun_b exch def
dup fun_b exch fun_a
dup 0 eq{pop pop pX mX sub pY mY sub add 100 add}{div}ifelse
}def
/pi{3.1415}bind def
/radians{180 mul pi div}def
%% converts radians to degrees
%% - postscript trig functions take degree arguments
/COS{ radians cos}def %% Radian versions of standard trig functions
/SIN{ radians sin}def
/TAN{ radians {sin}{cos} DIV}def
%% Any plotting function can have a sing_ prepended
%% This plots just as the non-sing version except that
%% each point is checked to see how far it is from the
%% previous point and if it is too far, we just moveto
%% the point rather than lineto it. This prevents lines
%% connecting jump discontinuities of the function.
%% (VERY steep parts may also be skipped.)
%% The sing_ version is slower than the non-sing version
%% and should only be used when the regular version shows
%% lines you don't want.
/PLOT{
/fun_v exch def %% Pops the parameter value and
%% pushes the xy-coordinates of the point
/end_v exch def
/inc_v exch def
/start_v exch def
start_v fun_v moveto %% moveto start
start_v inc_v end_v {fun_v lineto} for %% connect the dots
}def
/sing_PLOT{
/fun_v exch def
/end_v exch def
/inc_v exch def
/start_v exch def
start_v fun_v /last_y exch def /last_x exch def %% initialize last_?
last_x last_y moveto %% and move to there to start
start_v inc_v end_v { %% initialize for-loop
fun_v /next_y exch def /next_x exch def %% get next_?
next_x next_y %% arguments for lineto/moveto
0 last_y next_y sub abs pY sub mY add le{moveto}{ %% dy too big? moveto
0 last_x next_x sub abs pX sub mX add le{moveto}{ %% dx too big? moveto
lineto}ifelse}ifelse %% otherwise, lineto
/last_x next_x def/last_y next_y def %% shift next_? to last_?
} for
}def
%% Cartesian coordinate stuff
/XY{
%% Pops a parameter value off the stack and pushes the xy-coordinates
%% of the point in the current parameterized curve
dup XeqFun xTick mul exch YeqFun yTick mul
}def
/graph{
%% Just like Graph but XeqFun and YeqFun are reset to {}
%% This usually means that one can graph
%% y=f(x) by just defining YeqFun OR
%% x=f(y) by just defining XeqFun
%% USAGE: start_v increment_v end_v graph
Graph /XeqFun{}def /YeqFun{}def
}def
/Graph{
%% Takes the current definitions of XeqFun and YeqFun
%% and graphs the parameterized curve.
%% It is automatically scaled so that x=1 appears at the first
%% xTick and y=1 appears at the first yTick
%% USAGE: start_v increment_v end_v Graph
%% Will graph y=YeqFun(t) x=XeqFun(t) from start_v to end_v by drawing lines
%% between successive points with t increased by increment_v.
%% Needs to be stroked to see graph so we can use graph
%% to make paths.
%% XeqFun and YeqFun are retained.
{XY} PLOT
}def
/sing_graph{sing_Graph /XeqFun{}def /YeqFun{}def
}def
/sing_Graph{{XY} sing_PLOT}def
%% POLAR COORDINATE STUFF
/polarcoordinates{
%% pops r and theta from the stack and pushes x and y
dup 3 -1 roll dup 4 1 roll exch COS mul xTick mul 3 1 roll SIN mul yTick mul
}def
/RT{
%% Pops a parameter value off the stack and pushes the r\theta-coordinates
%% of the point in the current parameterized polar curve
dup ReqFun exch ThetaeqFun
}def
/XYpolar{
%% Pops a parameter value off the stack and pushes the xy-coordinates
%% of the point in the current parameterized polar curve
RT polarcoordinates
}def
/polar {
%% Takes the current definitions of ReqFun and ThetaeqFun
%% and graphs the parameterized curve in polar coordinates.
%% USAGE: start_v increment_v end_v polar
%% Just like Polar except /ReqFun and /ThetaeqFun
%% are reset to {}
Polar /ReqFun{}def /ThetaeqFun{}def
}def
/Polar {
%% Takes the current definitions of ReqFun and ThetaeqFun
%% and graphs the parameterized curve in polar coordinates.
%% Need to write functions /ReqFun and /ThetaeqFun
%% USAGE: start_v increment_v end_v Polar
{XYpolar} PLOT
}def
/sing_polar {
sing_Polar /ReqFun{}def /ThetaeqFun{}def
}def
/sing_Polar {
{XYpolar} sing_PLOT
}def
/axes{
newpath
mX 0 moveto
pX 0 lineto
stroke
0 mY moveto
0 pY lineto
stroke } def
/Xtick{
%% puts ticks along the x-axis from the origin
%% with displacement xTick until pX to the right and mX to the left
xTick xTick pX
{
0 moveto
0 tickSize rmoveto
0 tickSize -2 mul rlineto
}for
/nT{xTick -1 mul}def
nT nT mX
{
0 moveto
0 tickSize rmoveto
0 tickSize -2 mul rlineto
}for
stroke} def
/Ytick{
%% puts ticks along the y-axis from the origin
%% with displacement yTick until pY up and mY down
yTick yTick pY
{
0 exch moveto
tickSize 0 rmoveto
tickSize -2 mul 0 rlineto
}for
/nT{yTick -1 mul}def
nT nT mY
{
0 exch moveto
tickSize 0 rmoveto
tickSize -2 mul 0 rlineto
}for stroke
} def
/Show{true charpath }def %% use instead of show when writing self-writing labels
/label{ /opx{show}def /myshow{true charpath}def /myfill{}def LaBel}def
/Label{ /opx{exec}def /myshow{exec}def /myfill{fill}def LaBel}def
/LaBel{
%%Sticks an array of labels along axes.
%%Four variants
%%USEAGE: array (+x) label
%%USEAGE: array (-x) label
%%USEAGE: array (+y) label
%%USEAGE: array (-y) label
%%Puts elements of array along positive(+)/negative(-) x/y axis
%%starting at the origin.
%%Elements of array are just strings to be printed in the current font.
%%Use Label if the array elements print themselves. This is useful
%%for example if different elements of your string need to be printed
%%in different fonts.
%%EG: [ {CMMI (\31)show CMR(/2)show} ] prints pi over 2
/sxn exch def
/arrx exch def
0 1 arrx length 1 sub {
dup arrx exch get 0 0 moveto myshow
pathbbox /ur_y exch def/ur_x exch def/ll_y exch def/ll_x exch def
newpath
ur_x ll_x sub /my_x exch def
ur_y ll_y sub /my_y exch def
(+x) sxn eq
{dup xTick mul xTick add 0 moveto
my_x -2 div -1 tickSize mul vfont sub rmoveto
arrx exch get opx}if
(-x) sxn eq
{dup xTick mul xTick add -1 mul 0 moveto
my_x -2 div -1 tickSize mul vfont sub rmoveto
arrx exch get opx}if
(+y) sxn eq
{dup yTick mul yTick add 0 exch moveto
0 hfont sub tickSize sub my_x sub my_y -2 div rmoveto
arrx exch get opx}if
(-y) sxn eq
{dup yTick mul yTick add -1 mul 0 exch moveto
0 hfont sub tickSize sub my_x sub my_y -2 div rmoveto
arrx exch get opx}if
myfill}for}def
%%%%%%% data %%%%%%%%%
%%BoundingBox: -100 -100 100 100
%%BoundingBox: left-x lower-y right-x upper-y
%% COPY "BoundingBox" LINE TO TOP OF FILE
%%%%%%% Axes - generic values, reset as needed
/tickSize{3}def
/pX{100}def %% Positive x-axis length
/pY{100}def %% Positive y-axis length
/mX{-100}def %% Negative x-axis length
/mY{-100}def %% Negative y-axis length
/xTick{20} def %% tick length for x-axis
/yTick{20} def %% tick length for y-axis
/Narr{ [(-1) (-2) (-3) (-4) ]} def %% the negative labels
/Parr{ [(1) (2) (3) (4)]} def %% the positive labels
%%Page: 1 1
CMR %% Sets basic TEX font
.4 setlinewidth
/ReqFun{ 2 mul SIN 6.25 mul}def
newpath
0 .01 pi 2 div Polar
closepath
.5 setgray fill
newpath
pi .01 3 pi mul 2 div Polar
closepath
fill
newpath
0 0 moveto
11 pi mul 16 div XYpolar lineto
11 pi mul 16 div .01 13 pi mul 16 div Polar
0 0 lineto
closepath
fill
0 setgray
axes
.1 setlinewidth
Xtick
Ytick
Parr (+x) label
Parr (+y) label
Narr (-x) label
Narr (-y) label
0 .01 pi 2 mul polar stroke
showpage
restore