Intersecting a freeform surface with a general swept surface

Jun Kyung Seong, Ku Jin Kim, Myung Soo Kim, Gershon Elber, Ralph R. Martin

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)473-483
Number of pages11
JournalCAD Computer Aided Design
Volume37
Issue number5 SPEC.ISS.
DOIs
Publication statusPublished - 2005 Apr 15
Externally publishedYes

Fingerprint

Free-form Surface
Sweep
Intersection
Curve
Parametric Curves
Parametric Surfaces
Ruled Surface
Zero set
Rational Curves
Robust Algorithm
Polynomial equation
Algebraic curve
Convert
Parameter Space
Critical point
Efficient Algorithms
Topology
Computing
Polynomials

Keywords

  • Freeform surfaces
  • Ringed surfaces
  • Ruled surfaces
  • Surface-surface intersection
  • Swept surfaces

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering
  • Geometry and Topology

Cite this

Intersecting a freeform surface with a general swept surface. / Seong, Jun Kyung; Kim, Ku Jin; Kim, Myung Soo; Elber, Gershon; Martin, Ralph R.

In: CAD Computer Aided Design, Vol. 37, No. 5 SPEC.ISS., 15.04.2005, p. 473-483.

Research output: Contribution to journalArticle

Seong, JK, Kim, KJ, Kim, MS, Elber, G & Martin, RR 2005, 'Intersecting a freeform surface with a general swept surface', CAD Computer Aided Design, vol. 37, no. 5 SPEC.ISS., pp. 473-483. https://doi.org/10.1016/j.cad.2004.10.006
Seong, Jun Kyung ; Kim, Ku Jin ; Kim, Myung Soo ; Elber, Gershon ; Martin, Ralph R. / Intersecting a freeform surface with a general swept surface. In: CAD Computer Aided Design. 2005 ; Vol. 37, No. 5 SPEC.ISS. pp. 473-483.
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