Interval methods for ray casting implicit surfaces with affine arithmetic
by
Affonso de Cusatis Junior,
Luiz Henrique de Figueiredo,
Marcelo Gattass
Reprint from
Proceedings of
SIBGRAPI'99
, 65-71.
Copyright © 1999, IEEE Computer Press.
Abstract.
We study the performance of affine arithmetic as a replacement for
interval arithmetic in interval methods for ray casting implicit surfaces.
Affine arithmetic is a variant of interval arithmetic
designed to handle the dependency problem,
and which
has improved several interval algorithms in computer graphics.
Keywords:
image synthesis;
root location;
interval arithmetic;
range analysis;
self-validated computing
full version
·
full color images
·
affine arithmetic
·
interval computations
References
Some of the references cited in the paper are available on-line:
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Janeiro, 1997.
Sphere:
x2+y2+z2-1
= 0
Drop:
4(x2+y2)-(1+z)(1-z)3
= 0
Mitchell:
4(x4+(y2+z2)2)+17x2(y2+z2)-20(x2+y2+z2)+17
= 0
Torus:
(x2+y2+z2-1-0.25)2-4(x2+y2)
= 0
Double Torus:
(4x2(1-x2)-y2)2+z2-0.25
= 0
Six peak:
(3x2-y2)2y2-(x2+y2)4-z
= 0
Steiner:
x2y2+y2z2+z2x2+xyz
= 0
Last update:
Thu Oct 27 15:38:42 BRST 2011
by lhf.