In Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, eminent computer graphics and computational mechanics researchers provide a state-of-the-art overview of generalized barycentric coordinates. Commonly used in cutting-edge applications such as mesh parametrization, image warping, mesh deformation, and finite as well as boundary element methods, the theory of barycentric coordinates is also fundamental for use in animation and in simulating the deformation of solid continua. Generalized Barycentric Coordinates is divided into three sections, with five chapters each, covering the theoretical background, as well as their use in computer graphics and computational mechanics. A vivid 16-page insert helps illustrating the stunning applications of this fascinating research area.

Key Features:

  • Provides an overview of the many different types of barycentric coordinates and their properties.

  • Discusses diverse applications of barycentric coordinates in computer graphics and computational mechanics.

  • The first book-length treatment on this topic

part 1|93 pages

Theoretical Foundations

chapter 1|20 pages

Barycentric Coordinates and Their Properties

ByDmitry Anisimov

chapter 2|20 pages

Shape Quality for Generalized Barycentric Interpolation

ByAndrew Gillette, Alexander Rand

chapter 3|20 pages

Transfinite Barycentric Coordinates

ByAlexander G. Belyaev, Pierre-Alain Fayolle

chapter 4|14 pages

Barycentric Mappings*

ByTeseo Schneider

chapter 5|17 pages

A Primer on Laplacians

ByMax Wardetzky

part 2|82 pages

Applications in Computer Graphics

chapter 6|12 pages

Mesh Parameterization

ByBruno Lévy

chapter 7|25 pages

Planar Shape Deformation

ByOfir Weber

chapter 8|12 pages

Multi-Sided Patches via Barycentric Coordinates

ByScott Schaefer

chapter 9|10 pages

Generalized Triangulations

ByPooran Memari

chapter 10|20 pages

Self-Supporting Surfaces

ByEtienne Vouga

part 3|103 pages

Applications in Computational Mechanics

chapter 11|18 pages

Applications of Polyhedral Finite Elements in Solid Mechanics*

ByJoseph E. Bishop

chapter 12|31 pages

Extremely Large Deformation with Polygonal and Polyhedral Elements*

ByGlaucio H. Paulino, Heng Chi, Cameron Talischi, Oscar Lopez-Pamies

chapter 13|15 pages

Maximum-Entropy Meshfree Coordinates in Computational Mechanics

ByMarino Arroyo

chapter 14|17 pages


BySteffen Weißer

chapter 15|17 pages

Virtual Element Methods for Elliptic Problems on Polygonal Meshes

ByAndrea Cangiani, Oliver J. Sutton, Vitaliy Gyrya, Gianmarco Manzini