Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

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 illustrates the stunning applications of this fascinating research area.

Table of Contents

Section I. Theoretical Foundations
Chapter 1. Barycentric Coordinates And Their Properties
Chapter 2. Shape Quality For Generalized Barycentric Interpolation
Chapter 3. Transfinite Barycentric Coordinates
Chapter 4. Barycentric Mappings
Chapter 5. A Primer On Laplacians
Section II. Applications In Computer Graphics
Chapter 6. Mesh Parameterization
Chapter 7. Planar Shape Deformation
Chapter 8. Multi-sided Patches Via Barycentric Coordinates
Chapter 9. Generalized Triangulations
Chapter 10. Self-supporting Surfaces
Section III. Applications In Computational Mechanics
Chapter 11. Applications Of Polyhedral Finite Elements In Solid Mechanics
Chapter 12. Extremely Large Deformation With Polygonal And Polyhedral Elements
Chapter 13. Maximum-entropy Meshfree Coordinates In Computational Mechanics
Chapter 14. Bem-based Fem
Chapter 15. Virtual Element Methods For Elliptic Problems On Polygonal Meshes