Continuous Collision and Interference Detection for 3D Geometric Models

This paper describes a new approach to perform continuous collision and interference detection between a pair of arbitrarily complex objects moving according to general three-dimensional affine motions. Our approach, which does not require any envelope computations, recasts the problem of detecting collisions and computing the interfering subsets in terms of inherently parallel set membership classification tests of specific curves against the original (static) geometric representations. We show that our approach can compute the subsets of the moving objects that collide and interfere, as well as the times of collision, which has important applications in mechanical design and manufacturing. Our approach can be implemented for any geometric representation that supports curve-solid intersections, such as implicit and parametric representations. We describe an implementation of the proposed technique for solids given as a boundary representation (B-rep), and illustrate its effectiveness for several rigid and deformable moving objects bounded by tesselated and freeform surfaces of various complexities. Furthermore, we show that our approach can be extended to also identify the local and global self-intersections of the envelopes of the moving objects without requiring to compute these envelopes explicitly. The paper concludes by summarizing the proposed approach as well as reviewing relevant computational improvements that can decrease the computational cost of the prototype implementation by orders of magnitude.