A robust algorithm for finding the real intersections of three quadric surfaces

Authors:
Zhi-qiang Xu;Xiaoshen Wang;Xiao-diao Chen;Jia-guang Sun
Affiliations:
Department of Computer Science, Tsinghua University, Beijing 100084, China;Department of Mathematics and Statistics, University of Arkansas at Little Rock, AR 72204, USA;Department of Computer Science, Tsinghua University, Beijing 100084, China;School of Software, Tsinghua University, Beijing 100084, China
Venue:
Computer Aided Geometric Design
Year:
2005

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Abstract

By Bezout's theorem, three quadric surfaces have at most eight isolated intersections although they may have infinitely many intersections. In this paper, we present an efficient and robust algorithm, to obtain the isolated and the connected components of, or to determine the number of isolated real intersections of, three quadric surfaces by reducing the problem to computing the real intersections of two planar curves obtained by Levin's method.