Collision Between Deformable Objects Using Fast-Marching on Tetrahedral Models

Abstract

This paper presents an approach to handling collision between deformable objects using tetrahedral decomposition. The tetrahedral volumetric model is often used to simulate deformable objects that handle cuts and splits. Interaction between such objects in a complex environment is still an open problem in interactive simulation. This paper is mainly focused on obtaining a fast computation of a reliable penalty response. The method consists in using an approximated distance map to compute a penalty based response. We propose to compute the distances to the boundary using a modified 'Closest Point' algorithm derived from Fast Marching. The presented algorithm, inspired by the [FL01], has the advantage of computing rapidly the 'Closest Point' in the volumetric tetrahedral mesh without any use of an additional computation grid. From the resulting distance map a response is computed using a new "segment-in-object" response that offers more reliable results than the "point-in-object" generally used in previous works. Using this collision model, simulation at interactive rate can be considered in an environment composed of objects that can be deformed and cut.