cm26+@andrew.cmu.edu (Curt McDowell) (08/01/88)
Here's a picture a few readers of the the graphics newsgroup might like...
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%!
% Pyramidal Fractal in PostScript
%
% Draws a 3-D pyramid fractal, as
% seen in a popular text on Fractals
%
% Author: Curt.McDowell@andrew.cmu.edu
% Carnegie-Mellon University
%
72 72 scale
% User-Adjustable Parameters:
%
% Adjust viewing angle by modifying alpha and beta.
% The pyramid is originally seen level with the front edge.
% It is then rotated around the Z axis by alpha
% (front corner moving left), then around the Y (horizonal)
% axis by beta (top corner moving away).
/alpha -11 def /beta -10 def
/shadeleft 0.95 def /shaderight 0.5 def
/pagew 8.5 def /pageh 11 def
/StartSize 1.6 def /MinSize 0.2 def
0 -1 translate
/sina alpha sin def /sinb beta sin def
/cosa alpha cos def /cosb beta cos def
% Transformation from 3-D coordinates to 2-D
/xform % x,y,z ==> x',y'
{ /zz exch def
/yy exch def
/xx exch def
yy cosa mul xx sina mul sub
pagew 2 div mul % Compute X and
pagew 2 div add % leave on stack
xx sinb mul cosa mul yy sina mul sinb mul
add zz cosb mul add
pageh 2 div mul % Compute Y and
pageh 2 div add % leave on stack
} def
% Constants
/sqr3o4 3 sqrt 4 div def
/sqr3o2 3 sqrt 2 div def
/sqr3o6 3 sqrt 6 div def
/sqr6o3 6 sqrt 3 div def
/sqr3o12 3 sqrt 12 div def
/sqr6o6 6 sqrt 6 div def
/pyramid % x,y,z,size ==> --
{ /size exch def /z exch def /y exch def /x exch def
% (ax, ay) = Left bottom point
x y z
xform /ay exch def /ax exch def
% (bx, by) = bottom front point
sqr3o2 size mul x add size 2 div y add z
xform /by exch def /bx exch def
% (cx, cy) = Right bottom point
x size y add z
xform /cy exch def /cx exch def
% (dx, dy) = top point
sqr3o6 size mul x add size 2 div y add sqr6o3 size mul z add
xform /dy exch def /dx exch def
% Fill the 2 visible faces with different shades
ax ay moveto bx by lineto dx dy lineto closepath
shadeleft setgray fill
cx cy moveto bx by lineto dx dy lineto closepath
shaderight setgray fill
% Draw the 5 visible segments
0 setgray 0.1 72 div setlinewidth
ax ay moveto bx by lineto cx cy lineto dx dy lineto
closepath dx dy moveto bx by lineto stroke
} def
% Recursive routine to build a pyramid out of subpyramids
/buildsave { x y z size } def
/buildrest { /size exch def /z exch def /y exch def /x exch def } def
/build % x,y,z,size ==> --
{ /size exch def /z exch def /y exch def /x exch def
size MinSize lt
{ buildsave
x y z size pyramid
buildrest
}
{ buildsave
x y z size 2 div build
buildrest
buildsave
x size 2 div y add z size 2 div build
buildrest
buildsave
sqr3o12 size mul x add size 4 div y add
sqr6o6 size mul z add size 2 div build
buildrest
sqr3o4 size mul x add size 4 div y add
z size 2 div build
} ifelse
} def
0 StartSize -2 div StartSize sqr6o6 mul -2 div StartSize build
showpage
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Curt McDowell
Carnegie Mellon University
cm26@andrew.cmu.edu