An algorithm for triangulating multiple 3D polygons

We present an algorithm for obtaining a triangulation of multiple, non‐planar 3D polygons. The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles. Our algorithm generalizes a classical method for optimally triangulating a singl...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 5; pp. 157 - 166
Main Authors: Zou, Ming, Ju, Tao, Carr, Nathan
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2013
Subjects:
3-D graphics
Algorithms
Approximation
Computer graphics
Computer science
Feeding
Mathematical models
Optimization
Polygons
Studies
Three dimensional
Triangles
United States > US
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We present an algorithm for obtaining a triangulation of multiple, non‐planar 3D polygons. The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles. Our algorithm generalizes a classical method for optimally triangulating a single polygon. The key novelty is a mechanism for avoiding non‐manifold outputs for two and more input polygons without compromising optimality. For better performance on real‐world data, we also propose an approximate solution by feeding the algorithm with a reduced set of triangles. In particular, we demonstrate experimentally that the triangles in the Delaunay tetrahedralization of the polygon vertices offer a reasonable trade off between performance and optimality.
Bibliography:istex:FAB6C14719F9C82CBAD3F1E8782E948838658A0A
ArticleID:CGF12182
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12182