Modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting

Authors:
Huahao Shou;Hongwei Lin;Ralph R. Martin;Guojin Wang
Affiliations:
State Key Lab of CAD & CG, Zhejiang University, Hangzhou, China and Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, China;State Key Lab of CAD & CG, Zhejiang University, Hangzhou, China;School of Computer Science, Cardiff University, Cardiff, UK;State Key Lab of CAD & CG, Zhejiang University, Hangzhou, China
Venue:
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Year:
2006

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Abstract

This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than standard affine arithmetic when evaluating trivariate polynomials.