"Discrete Curvature for Physically-based Simulation and Shape Modeling"

Denis Zorin, Courant Institute of Mathematical Sciences New York University

Discrete curvature and shape operators, which capture complete information about directional curvatures at a point, are essential in a variety of applications: simulation of deformable surfaces (bending forces are determined by curvature), variational modeling and geometric data processing. In many of these applications, objects are represented by meshes. Solving mesh evolution or optimization problems involving discrete curvature may be expensive, as the dependence of discrete curvature on the vertex position is complex and highly nonlinear.

The quality of the results and computational efficiency is greatly influenced by the choice of curvature discretization. I will discuss mathematical tools for evaluating discretization quality and increasing discretization efficiency and their use in the context of physically-based simulation and geometric modeling...