Geometric computations in parameter space

Myung Soo Kim, Gershon Elber, Jun Kyung Seong

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

2 Citations (Scopus)

Abstract

We review a family of related techniques for geometric computations in the parameter space of freeform curves and surfaces. Geometric constraint equations for freeform curves and surfaces have low degrees (often linear or quadratic) in x,y,z and considerably higher degrees in the curve or surface parameters. We eliminate x,y, and z, so that the constraints are expressed in terms of the curve or surface parameters, while making the variables x,y,z the functions of these parameters under those same constraints. It is relatively straightforward to compute the differential geometric properties of many constructs using this representation. We have successfully addressed the following classes of computation for freeform curves and surfaces: Minkowski sums, bisectors and α-sectors, surface-surface intersections, collision detection, offset trimming, swept volume computation, constructing Voronoi diagrams, convex hulls and kernels, silhouette, and visibility computations. We provide a few simple examples to demonstrate how to apply this technique to a variety of problems in geometric computation.

Original languageEnglish
Title of host publicationSpring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings
Pages27-32
Number of pages6
Publication statusPublished - 2005 Dec 1
Externally publishedYes
EventSpring Conference on Computer Graphics, SCCG 2005 - Budmerice, Slovakia
Duration: 2006 May 122006 May 14

Other

OtherSpring Conference on Computer Graphics, SCCG 2005
CountrySlovakia
CityBudmerice
Period06/5/1206/5/14

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Keywords

  • Freeform curves and surfaces
  • Geometric constraints
  • Parameter space
  • System of polynomial equations

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Kim, M. S., Elber, G., & Seong, J. K. (2005). Geometric computations in parameter space. In Spring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings (pp. 27-32)

Geometric computations in parameter space. / Kim, Myung Soo; Elber, Gershon; Seong, Jun Kyung.

Spring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings. 2005. p. 27-32.

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

Kim, MS, Elber, G & Seong, JK 2005, Geometric computations in parameter space. in Spring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings. pp. 27-32, Spring Conference on Computer Graphics, SCCG 2005, Budmerice, Slovakia, 06/5/12.
Kim MS, Elber G, Seong JK. Geometric computations in parameter space. In Spring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings. 2005. p. 27-32
Kim, Myung Soo ; Elber, Gershon ; Seong, Jun Kyung. / Geometric computations in parameter space. Spring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings. 2005. pp. 27-32
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