Physically-based surface triangulation for parametric surfaces

Abstract

This thesis proposes an efficient physically-based method to generate a triangular mesh that approximates a parametric surface. As an approximation of the curvature characteristics of a surface region, we propose the curvature feature, that is a computationally simple but effective measure of the surface curvedness. In the proposed algorithm, the curvature feature of a surface region is regarded as an attracting force, and applied to a vertex using a spring model. The surface curvedness is distributed uniformly over the mesh by this algorithm. To determine the location of each vertex in the mesh, an initial triangulation is formed using the restricted quadtree and iteratively optimized based on the spring model. Since our approach uses a local optimization instead of a global optimization to determine the location of each vertex at each optimization step, a mesh can be generated fast enough for interactive applications.