Intersecting a freeform surface with a ruled or a ringed surface

Jun Kyung Seong, Ku Jin Kim, Myung Soo Kim, Gershon Elber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

We present efficient and robust algorithms for intersecting a freeform surface with a ringed surface or a ruled surface. A ringed surface is given as a one-parameter family of circles. By computing the intersection between a freeform surface and each circle 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; and the intersection curve is constructed by connecting them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of two polynomial equations in the parameter space. The intersection between a freeform surface and a ruled surface can be computed in a similar way.

Original languageEnglish
Title of host publicationProceedings - Geometric Modeling and Processing 2004
EditorsS.M. Hu, H. Pottmann
Pages38-45
Number of pages8
Publication statusPublished - 2004 Sep 29
Externally publishedYes
EventProceedings - Geometric Modeling and Processing 2004 - Beijing, China
Duration: 2004 Apr 132004 Apr 15

Other

OtherProceedings - Geometric Modeling and Processing 2004
CountryChina
CityBeijing
Period04/4/1304/4/15

Fingerprint

Topology
Polynomials

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Seong, J. K., Kim, K. J., Kim, M. S., & Elber, G. (2004). Intersecting a freeform surface with a ruled or a ringed surface. In S. M. Hu, & H. Pottmann (Eds.), Proceedings - Geometric Modeling and Processing 2004 (pp. 38-45)

Intersecting a freeform surface with a ruled or a ringed surface. / Seong, Jun Kyung; Kim, Ku Jin; Kim, Myung Soo; Elber, Gershon.

Proceedings - Geometric Modeling and Processing 2004. ed. / S.M. Hu; H. Pottmann. 2004. p. 38-45.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Seong, JK, Kim, KJ, Kim, MS & Elber, G 2004, Intersecting a freeform surface with a ruled or a ringed surface. in SM Hu & H Pottmann (eds), Proceedings - Geometric Modeling and Processing 2004. pp. 38-45, Proceedings - Geometric Modeling and Processing 2004, Beijing, China, 04/4/13.
Seong JK, Kim KJ, Kim MS, Elber G. Intersecting a freeform surface with a ruled or a ringed surface. In Hu SM, Pottmann H, editors, Proceedings - Geometric Modeling and Processing 2004. 2004. p. 38-45
Seong, Jun Kyung ; Kim, Ku Jin ; Kim, Myung Soo ; Elber, Gershon. / Intersecting a freeform surface with a ruled or a ringed surface. Proceedings - Geometric Modeling and Processing 2004. editor / S.M. Hu ; H. Pottmann. 2004. pp. 38-45
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