Intersecting a freeform surface with a general swept surface

Authors:
Joon-Kyung Seong;Ku-Jin Kim;Myung-Soo Kim;Gershon Elber;Ralph R. Martin
Affiliations:
School of Computer Science and Engineering, Seoul National University, Seoul 151-742, South Korea;Department of Computer Engineering, Kyungpook National University, Kyungpook, South Korea;School of Computer Science and Engineering, Seoul National University, Seoul 151-742, South Korea and Institute of Computer Technology, Seoul National University, Seoul, South Korea;Department of Computer Science, Technion, Haifa 32000, Israel;School of Computer Science, Cardiff University, South Wales, UK
Venue:
Computer-Aided Design
Year:
2005

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Abstract

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.