Trimming local and global self-intersections in offset curves/surfaces using distance maps

Joon Kyung Seong, Gershon Elber, Myung Soo Kim

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)

Abstract

A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented. Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset. By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected. The zero-set of polynomial equation(s) corresponds to the self-intersection regions. These regions are trimmed by projecting the zero-set into an appropriate parameter space. The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient. Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces. The effectiveness of our approach is demonstrated using several experimental results.

Original languageEnglish
Pages (from-to)183-193
Number of pages11
JournalCAD Computer Aided Design
Volume38
Issue number3
DOIs
Publication statusPublished - 2006 Mar
Externally publishedYes

Keywords

  • Distance map
  • Global self-intersection
  • Local self-intersection
  • Offset curve
  • Offset surface
  • Zero-set computation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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