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Intersecting a freeform surface with a general swept surface

Seong, Joon-Kyung, Kim, Ku-Jin, Kim, Myung-Soo, Elber, Gershon and Martin, Ralph Robert 2005. Intersecting a freeform surface with a general swept surface. Computer-Aided Design 37 (5) , pp. 473-483. 10.1016/j.cad.2004.10.006

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Uncontrolled Keywords: Surface–surface intersection; Swept surfaces; Ruled surfaces; Ringed surfaces; Freeform surfaces
Additional Information: PDF uploaded in accordance with publisher's policy http://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy [accessed 22/01/2015] NOTICE: this is the author’s version of a work that was accepted for publication in Computer-Aided Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer-Aided Design, [VOL 37, ISSUE 5, 2005 DOI: 10.1016/j.cad.2004.10.006
Publisher: Elsevier
ISSN: 0010-4485
Last Modified: 05 Jun 2017 01:18
URI: http://orca-mwe.cf.ac.uk/id/eprint/31775

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