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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input images5.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1994.
@
<<*>>=
<<license>>
-- Color gallery page 5
-- Etruscan Venus
-- Parameterization by George Frances
venus(a,r,steps) ==
surf := (u:DoubleFloat, v:DoubleFloat): Point DoubleFloat +->
cv := cos(v)
sv := sin(v)
cu := cos(u)
su := sin(u)
x := r * cos(2*u) * cv + sv * cu
y := r * sin(2*u) * cv - sv * su
z := a * cv
point [x,y,z]
draw(surf, 0..%pi, -%pi..%pi, var1Steps==steps,var2Steps==steps,
title == "Etruscan Venus")
venus(5/2, 13/10, 50)
-- Figure Eight Klein Bottle
-- Parameterization from:
-- "Differential Geometry and Computer Graphics" by Thomas Banchoff
-- in Perspectives in Mathemtaics, Anneversry of Oberwolfasch 1984.
-- Beirkhauser-Verlag, Basel, pp 43-60.
klein(x,y) ==
cx := cos(x)
cy := cos(y)
sx := sin(x)
sy := sin(y)
sx2 := sin(x/2)
cx2 := cos(x/2)
sq2 := sqrt(2.0@DoubleFloat)
point [cx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _
sx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _
-sx2 * (sq2 + cy) + cx2 * sy * cy]
draw(klein, 0..4*%pi, 0..2*%pi, var1Steps==50, var2Steps==50, _
title=="Figure Eight Klein Bottle")
-- Twisted torus
)read ntube
-- rotate a 2-d point by theta round the origin
rotateBy(p, theta) ==
c := cos(theta)
s := sin(theta)
point [p.1*c - p.2*s, p.1*s + p.2*c]
-- a circle in 3-space
bcircle t ==
point [3*cos t, 3*sin t, 0]
-- an elipse which twists around 4 times as t revolves once.
twist(u, t) ==
theta := 4*t
p := point [sin u, cos(u)/2]
rotateBy(p, theta)
ntubeDrawOpt(bcircle, twist, 0..2*%pi, 0..2*%pi, _
var1Steps == 70, var2Steps == 250)
-- Striped torus
-- a twisting circle
twist2(u, t) ==
theta := t
p := point [sin u, cos(u)]
rotateBy(p, theta)
-- color function producing 21 stripes
cf(u,v) == sin(21*u)
ntubeDrawOpt(bcircle, twist2, 0..2*%pi, 0..2*%pi, _
colorFunction == cf, var1Steps == 168, var2Steps == 126)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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