Robust tessellation of trimmed rational B-spline surface patches

Wonjoon Cho, Takashi Maekawa, Nicholas M. Patrikalakis, Jaime Peraire

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

5 Citations (Scopus)

Abstract

We present an unstructured triangular mesh generation algorithm that approximates a set of mutually non-intersecting simple trimmed rational B-spline surface patches within a user specified geometric tolerance. The proposed method uses numerically robust interval geometric representations/computations and also addresses the problem of topological consistency (homeomorphism) between the exact geometry and its approximation. Those are among the most important outstanding issues in geometry approximation problems. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is utilized to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed. Unstructured triangular meshes for free-form surfaces frequently involve triangles with high aspect ratio and accordingly, result in ill-conditioned meshing. Our proposed algorithm constructs 2D triangulation domains which sufficiently preserve the shape of triangles when mapped into 3D space and furthermore, the algorithm provides an efficient method that explicitly controls the aspect ratio of the triangular elements.

Original languageEnglish
Title of host publicationProceedings - Computer Graphics International, CGI 1998
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages543-555
Number of pages13
ISBN (Electronic)0818684453, 9780818684456
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes
Event1998 Computer Graphics International, CGI 1998 - Hannover, Germany
Duration: 1998 Jun 221998 Jun 26

Publication series

NameProceedings - Computer Graphics International, CGI 1998
Volume1998-January

Conference

Conference1998 Computer Graphics International, CGI 1998
CountryGermany
CityHannover
Period98/6/2298/6/26

Keywords

  • Homeomorphism
  • Robustness
  • Trimmed rational b-spline patch
  • Well-conditioned unstructured meshing

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Hardware and Architecture
  • Media Technology

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    Cho, W., Maekawa, T., Patrikalakis, N. M., & Peraire, J. (1998). Robust tessellation of trimmed rational B-spline surface patches. In Proceedings - Computer Graphics International, CGI 1998 (pp. 543-555). (Proceedings - Computer Graphics International, CGI 1998; Vol. 1998-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CGI.1998.694308