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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input antoine.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1994.
@
<<*>>=
<<license>>
-- Draw Antoine's Necklace
-- Thanks to Matt Grayson (formerly at IBM's T.J Watson Research Center)
-- for the idea.
-- Bring DH matrices into the environment
)set expose add con DenavitHartenbergMatrix
)read dhtri
-- The current transformation for drawing a sub-ring
torusRot: DHMATRIX(DoubleFloat)
-- Draw Antoine's Rings with n levels of recursive subdivision.
-- The number of subrings is 10**n.
drawRings(n) ==
s := create3Space()$ThreeSpace DoubleFloat
-- create an identity transformation
dh:DHMATRIX(DoubleFloat) := identity()
drawRingsInner(s, n, dh)
makeViewport3D(s, "Antoine's Necklace")
-- Recursively draw Antoine's Necklace.
drawRingsInner(s, n, dh) ==
n = 0 =>
drawRing(s, dh)
void()
t := 0.0@DoubleFloat -- the current angle around the ring
p := 0.0@DoubleFloat -- the angle of the subring from the plane
tr := 1.0@DoubleFloat -- the amount to translate the subring
inc := 0.1@DoubleFloat -- translation increment
-- subdivide the ring into 10 linked rings
for i in 1..10 repeat
tr := tr + inc
inc := -inc
dh' := dh * rotatez(t) * translate(tr, 0.0@DoubleFloat, 0.0@DoubleFloat) *
rotatey(p) * scale(0.35@DoubleFloat, 0.48@DoubleFloat, 0.4@DoubleFloat)
drawRingsInner(s, n-1, dh')
t := t + 36.0@DoubleFloat
p := p + 90.0@DoubleFloat
void()
-- draw a single ring into the given subspace, transformed by the given
-- DHMATRIX.
drawRing(s, dh) ==
free torusRot
torusRot := dh
makeObject(torus, 0..2*%pi, 0..2*%pi, var1Steps == 6, space == s,
var2Steps == 15)
-- Parameterization of a torus, transformed by the DHMATRIX in torusRot.
torus(u ,v) ==
cu := cos(u)/6
torusRot * point [(1+cu)*cos(v), (1+cu)*sin(v), (sin u)/6]
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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