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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input scherk.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1994.
@
<<*>>=
<<license>>
-- Scherk's minimal surface.
-- Defined by:
-- exp(z) * cos(x) = cos(y)
-- See: A comprehensive Introduction to Differential Geometry, Vol. 3,
-- by Michael Spivak, Publish Or Persih, Berkeley, 1979, pp 249-252.
-- Off set for a single piece of Scherk's minimal surface
(xOffset, yOffset):DoubleFloat
-- DrawScherk's minimal surface on an m by n patch.
drawScherk(m,n) ==
free xOffset, yOffset
space := create3Space()$ThreeSpace(DoubleFloat)
for i in 0..m-1 repeat
xOffset := i*%pi
for j in 0 .. n-1 repeat
rem(i+j, 2) = 0 => 'iter
yOffset := j*%pi
drawOneScherk(space)
makeViewport3D(space, "Scherk's Minimal Surface")
-- The four patches which make up a single piece of Scherk's minimal surface.
scherk1(u,v) ==
x := cos(u)/exp(v)
point [xOffset + acos(x), yOffset + u, v, abs(v)]
scherk2(u,v) ==
x := cos(u)/exp(v)
point [xOffset - acos(x), yOffset + u, v, abs(v)]
scherk3(u,v) ==
x := exp(v) * cos(u)
point [xOffset + u, yOffset + acos(x), v, abs(v)]
scherk4(u,v) ==
x := exp(v) * cos(u)
point [xOffset + u, yOffset - acos(x), v, abs(v)]
-- We draw the surface by breaking it into 4 patches, and drawing them
-- into a single space.
drawOneScherk(s) ==
makeObject(scherk1, -%pi/2..%pi/2, 0..%pi/2, space == s, _
var1Steps == 28, var2Steps == 28)
makeObject(scherk2, -%pi/2..%pi/2, 0..%pi/2, space == s, _
var1Steps == 28, var2Steps == 28)
makeObject(scherk3, -%pi/2..%pi/2, -%pi/2..0, space == s, _
var1Steps == 28, var2Steps == 28)
makeObject(scherk4, -%pi/2..%pi/2, -%pi/2..0, space == s, _
var1Steps == 28, var2Steps == 28)
void()
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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