Splines for Meshes with Irregularities
The SMAI journal of computational mathematics, Volume S5 (2019) , pp. 161-183.

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 n4 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: https://doi.org/10.5802/smai-jcm.57
Classification: 65N35,  15A15
Keywords: splines, irregular, classification
@article{SMAI-JCM_2019__S5__161_0,
     author = {J\"org Peters},
     title = {Splines for Meshes with Irregularities},
     journal = {The SMAI journal of computational mathematics},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {S5},
     year = {2019},
     pages = {161-183},
     doi = {10.5802/smai-jcm.57},
     language = {en},
     url = {smai-jcm.centre-mersenne.org/item/SMAI-JCM_2019__S5__161_0/}
}
Peters, Jörg. 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/item/SMAI-JCM_2019__S5__161_0/

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