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.
PART 1 – Theoretical foundations of barycentric coordinates. Ch1) Barycentric coordinates and their properties. Ch2)
Discrete Laplacians. Ch3) Gradient bounds for polyhedral Wachspress coordinates. Ch4) Bijective barycentric mappings. PART 2 –
Applications in Computer Graphics. Ch5) Mesh parameterization. Ch6) Planar shape deformation. Ch7) Character animation.
Ch8) Generalized triangulations. Ch9) Self-supporting surfaces. Ch10) Generalized Coons patches over arbitrary polygons
PART 3 – Applications in Computational Mechanics. Ch11) Local maximum-entropy approximation schemes for deformation of
solid continua. Ch12) A displacement-based finite element formulation for general polyhedra using harmonic coordinates. Ch13)
Mathematical analysis of polygonal and polyhedral finite element methods . Ch14) Polyhedral finite elements for topology
optimization. Ch15) Virtual element method for general second-order elliptic problems on polygonal meshes