Minimum distance between two sphere-swept surfaces

Kwanhee Lee, Jun Kyung Seong, Ku Jin Kim, Sung Je Hong

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We present an efficient and robust approach for computing the minimum distance between two sphere-swept surfaces. As examples of sphere-swept surfaces, we consider canal surfaces and bivariate sphere-swept surfaces. For computing the minimum distance between two parametric surfaces, a simple technique is to find the two closest points from the given surfaces using the normal vector information. We suggest a novel approach that efficiently computes the minimum distance between two sphere-swept surfaces by treating each surface as a family of spheres. Rather than computing the complicated normal vectors for given surfaces, our method solves the problem by computing the minimum distance between two moving spheres. We prove that the minimum distance between two sphere-swept surfaces is identical to that between two moving spheres. Experimental results of minimum distance computation are given. We also reproduce the result of Kim [Kim K-J. Minimum distance between a canal surface and a simple surface. Computer-Aided Design 2003;35:871-9] based on the suggested approach.

Original languageEnglish
Pages (from-to)452-459
Number of pages8
JournalCAD Computer Aided Design
Volume39
Issue number6
DOIs
Publication statusPublished - 2007 Jun 1
Externally publishedYes

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Keywords

  • Bivariate sphere-swept surface
  • Canal surface
  • Distance
  • Sphere geometry

ASJC Scopus subject areas

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

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