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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Vydáno v:Computer graphics forum Ročník 32; číslo 5; s. 157 - 166
Hlavní autoři: Zou, Ming, Ju, Tao, Carr, Nathan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford, UK Blackwell Publishing Ltd 01.08.2013
Témata:
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
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Shrnutí: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.
Bibliografie:istex:FAB6C14719F9C82CBAD3F1E8782E948838658A0A
ArticleID:CGF12182
ark:/67375/WNG-D5BT45VC-D
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12182