The surface/surface intersection problem by means of matrix based representations

Authors:
Laurent Busé;Thang Luu Ba
Affiliations:
INRIA, Galaad, 2004 route des Lucioles, 06902 Sophia Antipolis, France;INRIA, Galaad, 2004 route des Lucioles, 06902 Sophia Antipolis, France and Hanoi National University of Education, Department of Mathematics, 136 Xuan Thuy, Cau Giay, Hanoi, Viet Nam
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

Evaluating the intersection of two rational parameterized algebraic surfaces is an important problem in solid modeling. In this paper, we make use of some generalized matrix based representations of parameterized surfaces in order to represent the intersection curve of two such surfaces as the zero set of a matrix determinant. As a consequence, we extend to a dramatically larger class of rational parameterized surfaces, the applicability of a general approach to the surface/surface intersection problem due to J. Canny and D. Manocha. In this way, we obtain compact and efficient representations of intersection curves allowing to reduce some geometric operations on such curves to matrix operations using results from linear algebra.