Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics (Hardcover)

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