Generalized triangulations

Pooran Memari

doi:10.1201/9781315153452

Generalized triangulations

Pooran Memari

Université Paris-Saclay

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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.

Original language	English
Title of host publication	Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics
Publisher	CRC Press
Pages	147-156
Number of pages	10
ISBN (Electronic)	9781498763615
ISBN (Print)	9781498763592
DOIs	https://doi.org/10.1201/9781315153452
Publication status	Published - 1 Jan 2017
Externally published	Yes

Access to Document

10.1201/9781315153452

Cite this

@inbook{56c7f1adb4be4accaa8f3bdfce4028eb,

title = "Generalized triangulations",

abstract = "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.",

author = "Pooran Memari",

note = "Publisher Copyright: {\textcopyright} 2018 by Taylor \& Francis Group, LLC.",

year = "2017",

month = jan,

day = "1",

doi = "10.1201/9781315153452",

language = "English",

isbn = "9781498763592",

pages = "147--156",

booktitle = "Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics",

publisher = "CRC Press",

}

TY - CHAP

T1 - Generalized triangulations

AU - Memari, Pooran

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

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.

U2 - 10.1201/9781315153452

DO - 10.1201/9781315153452

M3 - Chapter

AN - SCOPUS:85052588406

SN - 9781498763592

SP - 147

EP - 156

BT - Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

PB - CRC Press

ER -

Generalized triangulations

Abstract

Access to Document

Fingerprint

Cite this