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 coordinatesis 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 – 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

Kai Hormann is a full professor in the Faculty of Informatics at USI (Università della Svizzera italiana). His research interests are focused on the mathematical foundations of geometry processing algorithms as well as their applications in computer graphics and related fields. In particular, he is working on generalized barycentric coordinates, subdivision of curves and surfaces, barycentric rational interpolation, and dynamic geometry processing. N Sukumar is a full professor in the Department of Civil and Environmental Engineering at UC Davis. His research interests are in the areas of computational solid mechanics and applied mathematics, with emphasis on developing and advancing modern finite element and meshfree methods for applications in the deformation and fracture of solids and in ab initio quantum-mechanical materials calculations.