Geometric computations in parameter space

Myung Soo Kim, Gershon Elber, Joon Kyung Seong

Research output: Contribution to conferencePaper

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
Pages27-32
Number of pages6
Publication statusPublished - 2005
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

Keywords

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

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Kim, M. S., Elber, G., & Seong, J. K. (2005). Geometric computations in parameter space. 27-32. Paper presented at Spring Conference on Computer Graphics, SCCG 2005, Budmerice, Slovakia.