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


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Full color images

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.