%!
% Warp an image.
% By Don Hopkins and Rehmi Post
% Input is a function to execute that produces the image in a unit square,
% and two arrays of numbers describing the horizontal and vertical
% partitioning of the source image.

/warp	% hparts vparts showit ==> ---
{   /showit exch def
    /vparts exch normalize def
    /hparts exch normalize def
    /n hparts length def
    /m vparts length def
    /hstep 1 n div def
    /vstep 1 m div def
    /yloc 0 def

    0  1  m 1 sub { /j exch def
	/xloc 0 def

        0  1  n 1 sub { /i exch def
	    gsave showsquare grestore

	    /xloc  xloc hpart add  def
        } for

	/yloc  yloc vpart add  def
    } for
} def

/normalize  % array ==> normalized_array
{   0  1 index  { add } forall
    /total exch def
    [ exch { total div } forall ]
} def

/showsquare % --- ==> ---
{   /hloc  hstep i mul  def
    /vloc  vstep j mul  def
    /hpart  hparts i get  def
    /vpart  hparts j get  def

    % Clip to the destination square
    newpath
      hloc  vloc  moveto
      hloc  vloc vstep add  lineto
      hloc hstep add  vloc vstep add  lineto
      hloc hstep add  vloc  lineto
    closepath
    clip

    % Translate and scale so that the source square is mapped onto
    % the destination square
    hloc vloc translate
    hpart  hstep  div
    vpart  vstep  div  scale
    xloc neg  yloc neg  translate

    % Produce the image
    showit
} def

/circles    % --- ==> ---
{   newpath
    0 .1 .5 {
	.5 exch .5 exch 0 360 arc } for

    0 setgray
    .005 setlinewidth
    stroke
} def

/grid    % --- ==> ---
{   newpath
    0 .1 1 { /x exch def
        x 0 moveto  x 1 lineto  stroke
        0 x moveto  1 x lineto  stroke
    } for

    0 setgray
    .03 setlinewidth
    stroke
} def

gsave
  50 50 translate
  300 300 scale
  [2 5 3] [1 3 6] 
  { grid circles } warp
grestore

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