Topologically reliable approximation of trimmed polynomial surface patches

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

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We present an unstructured triangular mesh generation algorithm that approximates a set of mutually nonintersecting simple trimmed polynomial parametric 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. We also extract important differential geometric features of input geometry for use in the approximation. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is introduced to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed and furthermore, an efficient method to compute a tight upper bound of the approximation error is proposed. 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
Pages (from-to)84-109
Number of pages26
JournalGraphical Models and Image Processing
Volume61
Issue number2
DOIs
Publication statusPublished - 1999 Mar 1
Externally publishedYes

Fingerprint

Patch
Polynomials
Triangulation
Polynomial
Triangular Mesh
Unstructured Mesh
Approximation
Aspect Ratio
Tolerance
Triangle
Geometry
Aspect ratio
Parametric Surfaces
Geometric Representation
Free-form Surface
Triangular Element
Tessellation
Approximate Algorithm
Delaunay triangulation
Delaunay

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design

Cite this

Topologically reliable approximation of trimmed polynomial surface patches. / Cho, Wonjoon; Maekawa, Takashi; Patrikalakis, Nicholas M.; Peraire, Jaime.

In: Graphical Models and Image Processing, Vol. 61, No. 2, 01.03.1999, p. 84-109.

Research output: Contribution to journalArticle

Cho, Wonjoon ; Maekawa, Takashi ; Patrikalakis, Nicholas M. ; Peraire, Jaime. / Topologically reliable approximation of trimmed polynomial surface patches. In: Graphical Models and Image Processing. 1999 ; Vol. 61, No. 2. pp. 84-109.
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