Generalized triangulations

Pooran Memari

doi:10.1201/9781315153452

Generalized triangulations

Pooran Memari

Université Paris-Saclay

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Résumé

The main concept of barycentric coordinates is intimately linked to the duality between primal and dual complexes. This chapter presents a general framework in ℝ^d to define a family of compatible dual complexes for a given triangulation. We derive a combinatorial characterization theorem for triangulations that admit a compatible, possibly non-orthogonal dual complex. We show how the mesh optimization methods in geometric modeling can benefit from the parameterization of the space of generalized triangulations.

langue originale	Anglais
titre	Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics
Editeur	CRC Press
Pages	147-156
Nombre de pages	10
ISBN (Electronique)	9781498763615
ISBN (imprimé)	9781498763592
Les DOIs	https://doi.org/10.1201/9781315153452
état	Publié - 1 janv. 2017
Modification externe	Oui

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10.1201/9781315153452

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AB - The main concept of barycentric coordinates is intimately linked to the duality between primal and dual complexes. This chapter presents a general framework in ℝd to define a family of compatible dual complexes for a given triangulation. We derive a combinatorial characterization theorem for triangulations that admit a compatible, possibly non-orthogonal dual complex. We show how the mesh optimization methods in geometric modeling can benefit from the parameterization of the space of generalized triangulations.

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Generalized triangulations

Résumé

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