research-article

Curvature-Dependent Triangulation of Implicit Surfaces

Authors:

Tasso Karkanis,

A. James StewartAuthors Info & Claims

IEEE Computer Graphics and Applications, Volume 21, Issue 2

Pages 60 - 69

https://doi.org/10.1109/38.909016

Published: 01 March 2001 Publication History

Abstract

This article describes an algorithm to generate a triangulation of an implicit surface. The generated triangles are close to equilateral and the triangle edge lengths vary with local surface curvature (the user may choose the ratio of edge length to surface curvature). The output of this algorithm is useful for applications that require high-quality triangulations, such as medical imaging, molecular modeling, computer aided design, and finite element analysis. Triangles are "grown" on the surface outward from a seed triangle. After the growing stops, the remaining gap in the triangulation is filled by a set of heuristics. Experiments show that the algorithm consistently builds high-quality triangulations, which compare favorably to those produced by cell-based and particle-based algorithms.

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Cited By

Hsieh MShell DLi SDantam N(2023)A sampling and learning framework to prove motion planning infeasibilityInternational Journal of Robotics Research10.1177/0278364923115467442:10(938-956)Online publication date: 15-Nov-2023
https://dl.acm.org/doi/10.1177/02783649231154674
Shen TMunkberg JHasselgren JYin KWang ZChen WGojcic ZFidler SSharp NGao J(2023)Flexible Isosurface Extraction for Gradient-Based Mesh OptimizationACM Transactions on Graphics10.1145/359243042:4(1-16)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592430
Zhang SWu WWei W(2022)An Intelligent Identification and Repair Method for Annular Holes in 3D PrintingComputational Intelligence and Neuroscience10.1155/2022/39902162022Online publication date: 1-Jan-2022
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Index Terms

Curvature-Dependent Triangulation of Implicit Surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Approximation algorithms

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Information

Published In

cover image IEEE Computer Graphics and Applications

IEEE Computer Graphics and Applications Volume 21, Issue 2

March 2001

91 pages

ISSN:0272-1716

Issue’s Table of Contents

Copyright © Copyright © 2001 IEEE. All Rights Reserved.

Publisher

IEEE Computer Society Press

Washington, DC, United States

Publication History

Published: 01 March 2001

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Cited By

Hsieh MShell DLi SDantam N(2023)A sampling and learning framework to prove motion planning infeasibilityInternational Journal of Robotics Research10.1177/0278364923115467442:10(938-956)Online publication date: 15-Nov-2023
https://dl.acm.org/doi/10.1177/02783649231154674
Shen TMunkberg JHasselgren JYin KWang ZChen WGojcic ZFidler SSharp NGao J(2023)Flexible Isosurface Extraction for Gradient-Based Mesh OptimizationACM Transactions on Graphics10.1145/359243042:4(1-16)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592430
Zhang SWu WWei W(2022)An Intelligent Identification and Repair Method for Annular Holes in 3D PrintingComputational Intelligence and Neuroscience10.1155/2022/39902162022Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1155/2022/3990216
Zhang SWei WWu W(2022)Research on an Intelligent Identification and Classification Method of Complex Holes in Triangle Meshes for 3D PrintingComputational Intelligence and Neuroscience10.1155/2022/22499252022Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1155/2022/2249925
de Araújo BLopes DJepp PJorge JWyvill B(2015)A Survey on Implicit Surface PolygonizationACM Computing Surveys10.1145/273219747:4(1-39)Online publication date: 26-May-2015
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Jung WPark SShin H(2015)Combining volumetric dental CT and optical scan data for teeth modelingComputer-Aided Design10.1016/j.cad.2015.04.00867:C(24-37)Online publication date: 1-Oct-2015
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Dey TJanoos FLevine J(2012)Meshing interfaces of multi-label data with Delaunay refinementEngineering with Computers10.5555/3226247.322643628:1(71-82)Online publication date: 1-Jan-2012
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Bronson JLevine JWhitaker R(2012)Particle systems for adaptive, isotropic meshing of CAD modelsEngineering with Computers10.1007/s00366-012-0266-x28:4(331-344)Online publication date: 1-Oct-2012
https://dl.acm.org/doi/10.1007/s00366-012-0266-x
Jepp PAraujo BJorge JWyvill BSousa M(2009)Style nodes and repolygonization for hierarchical tree-based implicit surface modellingProceedings of the Fifth Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging10.5555/2381286.2381294(41-48)Online publication date: 28-May-2009
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Fournier MDischler JBechmann D(2009)Marching triangle polygonization for efficient surface reconstruction from its distance transformProceedings of the 15th IAPR international conference on Discrete geometry for computer imagery10.5555/1813270.1813288(168-179)Online publication date: 30-Sep-2009
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