#
Tile.ps

Below is the text of the postscript file `tile.ps`, which
can be found in the directory `/u/cl/lib/postscript` The
corresponding picture is a tiling of the hyperbolic plane by
ideal triangles. See the
previous page
for directions on how to view a postscript file.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEFINITIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% set inch scale and line width
/inch {72 mul} def % define one inch
0.1 setlinewidth
% define parameters of figure:
/R 2.5 inch def % the scale: radius of limit circle
/a 60 def % the central half-angle
/b 90 a sub 2 mul def % the angle subtended by the arc
/c a 2 mul def % the angle of rotation
/r R a sin a cos div mul def % initial radius
/n 3 def % the number of arcs
/N 7 def % number of layers
% define basic arc (rotate after drawing it to get ready for next one):
/ARC {
r R r 180 180 b add arc
stroke
c rotate
} def
% procedure to update parameters for successive layers of tiling:
/update {
/a a 2 div def % update a: a <== a/2
/b 90 a sub 2 mul def % update b: b <== (90 - a)/2
/c a 2 mul def % update c: c <== 2a
/r R a sin a cos div mul def % update r: r <== R tan a
/n n 2 mul def % update n: n <== 2n
} def
%%%%%%%%%%%%%%%%%%%%% NOW DRAW THE FIGURE %%%%%%%%%%%%%%%%%%%%%
gsave % save graphics state
4.25 inch 6.0 inch translate % put origin near center of page
% draw unit circle:
newpath
0 0 R 0 360 arc stroke
% draw first layer of arcs:
1 1 n {ARC} for
% finally, draw N-1 more layers:
1 1 N 1 sub {
update
1 1 n {ARC} for
} for
grestore % restore graphics state
%%%%%%%%%%%%%%%%%%%%% FINALLY, ADD LEGEND %%%%%%%%%%%%%%%%%%%%%
/Times-BoldItalic findfont
36 scalefont
setfont
1.5 inch 1.5 inch moveto
(Tiling of Hyperbolic Plane) show
showpage