MS Kim: Accelerating Geometric Algorithms for Freeform Surfaces using Toroidal Patch Approximation

Myung Soo Kim, Seoul National University, Computer Science and Engineering Department We present a new approach to the acceleration of geometric algorithms for freeform surfaces using a hierarchy of bounding volumes, including those based on the osculating toroidal patches to the surfaces. Using this approach, we revisit some non-trivial conventional geometric algorithms, including those for computing the minimum and Hausdorff distances, the intersection and self-intersection curves, and the integral properties of freeform geometric models. We demonstrate the effectiveness of torus-based geometric computation, by reporting improvement in the speed, stability, and robustness of these algorithms.