Splines for Meshes with Irregularities

Jörg Peters

doi:10.5802/smai-jcm.57

Jörg Peters ¹

¹ Dept CISE, University of Florida, Gainesville FL 32611-6120, USA

The SMAI Journal of computational mathematics, Volume S5 (2019), pp. 161-183.

Abstract

Splines form an elegant bridge between the continuous real world and the discrete computational world. Their tensor-product form lifts many univariate properties effortlessly to the surfaces, volumes and beyond. Irregularities, where the tensor-structure breaks down, therefore deserve attention – and provide a rich source of mathematical challenges and insights.

This paper reviews and categorizes techniques for splines on meshes with irregularities. Of particular interest are quad-dominant meshes that can have $n \neq 4$ valent interior points and T-junctions where quad-strips end. “Generalized” splines can use quad-dominant meshes as control nets both for modeling geometry and to support engineering analysis without additional meshing.

Published online: 2020-01-29

DOI: 10.5802/smai-jcm.57

Classification: 65N35, 15A15
Keywords: splines, irregular, classification

Author's affiliations:

Jörg Peters ¹

¹ Dept CISE, University of Florida, Gainesville FL 32611-6120, USA

License:

CC-BY-NC-ND 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {J\"org Peters},
     title = {Splines for {Meshes} with {Irregularities}},
     journal = {The SMAI Journal of computational mathematics},
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Jörg Peters. Splines for Meshes with Irregularities. The SMAI Journal of computational mathematics, Volume S5 (2019), pp. 161-183. doi : 10.5802/smai-jcm.57. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.57/

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