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Perfect Laplacians for Polygon Meshes
Author(s) -
Herholz Philipp,
Kyprianidis Jan Eric,
Alexa Marc
Publication year - 2015
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12709
Subject(s) - polygon mesh , polygon (computer graphics) , volume mesh , embedding , mathematics , laplace operator , computer science , combinatorics , algorithm , mesh generation , geometry , mathematical analysis , finite element method , artificial intelligence , telecommunications , physics , frame (networking) , thermodynamics
A discrete Laplace‐Beltrami operator is called perfect if it possesses all the important properties of its smooth counterpart. It is known which triangle meshes admit perfect Laplace operators and how to fix any other mesh by changing the combinatorics. We extend the characterization of meshes that admit perfect Laplacians to general polygon meshes. More importantly, we provide an algorithm that computes a perfect Laplace operator for any polygon mesh without changing the combinatorics, although, possibly changing the embedding. We evaluate this algorithm and demonstrate it at applications.