Particle system for fast and precise collision detection. / Topological coding and shape recognition.

First, we will present recent work in developing methods for collision detection between complex geometric objects represented by polygonal models and undergoing rigid motions. Most algorithms described in the literature are based on some kind of hierarchical representations. An alternative approach has been recently proposed. The algorithm relies on the idea of “sensor” particles. Two types of particles that interact in a special way are used for determining the minimum distance between two models. The algorithm has been implemented and used in real-time simulation of dynamic interaction between geometric objects. However, the results of collision detection are not sufficiently precise to be used for CAD applications. We will talk about combining the particle system with some kind of hierarchical representation to achieve fast and precise collision detection. Also we will demonstrate how the particle system can be used for fast hierarchical building convex hulls for polygonal models.
In the second part of this talk, we will discuss a novel topological approach for shape coding and recognition. Topology matching and 3D shape classification are fundamental problems in computer vision, computer graphics, and medical imaging fields. While a lot of techniques for shape recognition have recently been proposed, they are generally restricted to their specific applications. The proposed approach is based on the fact that the most complete information about topological structure of the surface can be obtained by using labeled Reeb graphs or topological atoms and molecules. Having molecules corresponding to different shapes we apply a new statistical method to detect similarities between the shapes.