Interval implicitization of parametric surfaces

Authors:
Ning Li;Jing Jiang;Wenfeng Wang
Affiliations:
School of Statistics and Mathematics, Shandong Finance University, Jinan, China and Department of Mathematics, Shanghai University, Shanghai, China;Department of Mathematics, Qilu Normal College, Jinan, China;Department of Automatic, Research Center of Automatic Control, Binzhou College, Binzhou, China
Venue:
ICICA'10 Proceedings of the First international conference on Information computing and applications
Year:
2010

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Abstract

The interval implicit representations of parametric surfaces have wide applications in Computer Graphics, Geometric Modelling, and others. Based on the properties of interval algebraic surfaces, barycentric coordinates and Bernstein basis functions, this paper presents an algorithm to compute the interval implicit representation of a rational Bézier surface by solving an optimal problem with a quadratic object function and linear constraints. This problem is equivalent to finding the two bounding surfaces of the interval implicit surface. An example is provided to demonstrate the algorithm.