Pattern-Based Quadrangulation for N-Sided Patches

We propose an algorithm to quadrangulate an N‐sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns...

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Vydáno v:Computer graphics forum Ročník 33; číslo 5; s. 177 - 184
Hlavní autoři: Takayama, Kenshi, Panozzo, Daniele, Sorkine-Hornung, Olga
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.08.2014
Témata:
Algorithms
Analysis
and systems
Boundaries
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
Computer programming
I.3.3 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms
I.3.3 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
Integers
languages
Mathematical models
Simplification
Studies
Subdivisions
Topological manifolds
Topology
ISSN:0167-7055, 1467-8659
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Shrnutí:We propose an algorithm to quadrangulate an N‐sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch‐based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.
Bibliografie:ArticleID:CGF12443
Supporting Information
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SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12443