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|\^/| Maple 7 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc.
\ MAPLE / All rights reserved. Maple is a registered trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
# ellipsoid.maple -- compute equations for offset ellipsoid setup
# $Header: /usr/local/svn/cvs-repositories/numrelcvs/AEIThorns/AHFinderDirect/archive/ellipsoid.out,v 1.1 2002-07-18 17:37:11 jthorn Exp $
>
#
# ellipsoid has center (A,B,C), radius (a,b,c)
# angular coordinate system has center (U,V,W)
#
# direction cosines wrt angular coordinate center are (alpha,beta,gamma)
# but Maple predefines gamma = Euler's constant, so we use (xcos,ycos,zcos)
# instead, i.e. a point has coordinates (U+xcos*r, V+ycos*r, W+zcos*r)
#
# then the equation of the ellipsoid is
# (U+xcos*r - A)^2 (V+ycos*r - B)^2 (W+zcos*r - C)^2
# ----------------- + ---------------- + ----------------- = 1
# a^2 b^2 c^2
#
# to solve this, we introduce intermediate variables
# AU = A - U
# BV = B - V
# CW = C - W
#
> eqn := (xcos*r - AU)^2/a^2 + (ycos*r - BV)^2/b^2 + (zcos*r - CW)^2/c^2 = 1;
2 2 2
(xcos r - AU) (ycos r - BV) (zcos r - CW)
eqn := -------------- + -------------- + -------------- = 1
2 2 2
a b c
>
> read "../maple/util.mm";
Error, unable to read `../maple/util.mm`
> quit
bytes used=129844, alloc=196572, time=0.03
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