Fast proximity computation among deformable models using discrete Voronoi diagrams

Avneesh Sud, Naga Govindaraju, Russell Gayle, Ilknur Kabul, Dinesh Manocha
2006 ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06  
Figure 1 : Multiple deformable models simulation: This sequence shows the positions of the objects at three time instances in a simulation. The environment initially consists of 10 deforming objects represented using 5.5K triangles. As the simulation proceeds, the objects break into 25 sub-objects. Our algorithm is able to perform collision and separation distance computations, including self-collisions, among dynamically generated objects within 120 ms on a high-end PC. Abstract We present
more » ... ract We present novel algorithms to perform collision and distance queries among multiple deformable models in dynamic environments. These include inter-object queries between different objects as well as intra-object queries. We describe a unified approach to compute these queries based on N-body distance computation and use properties of the 2 nd order discrete Voronoi diagram to perform N-body culling. Our algorithms involve no preprocessing and also work well on models with changing topologies. We can perform all proximity queries among complex deformable models consisting of thousands of triangles in a fraction of a second on a high-end PC. Moreover, our Voronoi-based culling algorithm can improve the performance of separation distance and penetration queries by an order of magnitude. Main Results We present novel algorithms for fast proximity computation among multiple deformable models. Our approach involves no preprocessing and is applicable to all triangulated models undergoing nonrigid motion. In order to perform different proximity queries in complex environments, we present three key results: N-body distance query: We introduce a unified approach to perform different proximity queries using N-body distance computation: given a set P of primitives, for each primitive pi we compute the closest primitive in P \ {pi}. We also present efficient algorithms for continuous collision detection and local penetration depth computation based on the N-body distance query. Voronoi-based culling: We use properties of Voronoi diagrams to perform the N-body distance query efficiently. The closest primitive to any primitive (pi) is one of the Voronoi neighbors of pi. Therefore, the Voronoi diagram of primitives is an efficient data structure to perform N-body distance culling. We use the 2 nd order Voronoi diagram because it provides information about two closest primitives at each point in space and results in a higher culling efficiency. Fast and conservative computations using discrete Voronoi diagrams: The exact computation of continuous 3D Voronoi diagrams for general triangulated models is a hard problem. Instead, we compute discrete Voronoi diagrams on a uniform grid using graphics hardware. We exploit properties of the 2 nd order Voronoi diagram to derive distance error bounds that take into account discretization and sampling errors in discrete Voronoi diagrams. We use the distance bounds to efficiently compute the closest primitive at objectspace precision i.e. IEEE 64-bit floating point accuracy.
doi:10.1145/1179352.1142006 fatcat:qtzshlke45a2zm4sudle4v6cxy