Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

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.

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