We present an interactive algorithm for continuous collision detection between a moving avatar and its surrounding virtual environment. Our algorithm is able to compute the first time of contact between the avatar and the environment interactively, and also guarantees within a user-provided error threshold that no collision ever happens before the first contact occurs. We model the avatar as an articulated body using line skeletons with constant offsets and the virtual environment as a collection of polygonized objects. Given the position and orientation of the avatar at discrete time steps, we use an arbitrary in-between motion to interpolate the path for each link between discrete instances. We bound the swept space of each link using interval arithmetic and dynamically compute a bounding volume hierarchy (BVH) to cull links that are not in close proximity to the objects in the virtual environment. The swept volumes (SVs) of the remaining links are used to check for possible interference and estimate the time of collision between the surface of the SV and the rest of the objects. Furthermore, we use graphics hardware to accelerate collision queries on the dynamically generated swept surfaces. Our approach requires no precomputation and is applicable to general articulated bodies that do not contain a loop. We have implemented the algorithm on a 2.8 GHz Pentium IV PC with an NVIDIA GeForce 6800 Ultra graphics card and applied it to an avatar with 16 links, moving in a virtual environment composed of hundreds of thousands of polygons. Our prototype system is able to detect all contacts between the moving avatar and the environment in 10–30 ms.

We present a fast collision culling algorithm for performing inter- and intra-object collision detection among complex models using graphics hardware. Our algorithm utilizes visibility queries on the GPUs to eliminate a subset of geometric primitives that are not in close proximity and computes a potentially colliding set (PCS) of primitives. We perform no precomputation and the algorithm proceeds in multiple stages: object-level PCS computation, subobject level PCS computation, followed by exact collision detection. We extend our PCS computation algorithm to perform intra-object or self-collisions between complex models. Furthermore, we describe a novel visibility-based classification scheme to reduce the size of potentially-colliding sets of objects and primitives, and the number of visibility queries for further improving the performance and culling efficiency. We have implemented our algorithm on a PC with an NVIDIA GeForce FX 6800 Ultra graphics card and applied it to three complex simulations, each consisting of objects with tens of thousands of triangles. In practice, we are able to compute all the self-collisions for cloth simulation up to image-space precision at interactive rates.

We present a novel six-degree-of-freedom haptic rendering algorithm using incremental and localized contact computations. It uses an incremental approach for contact and force computations and takes advantage of spatial and temporal coherence between successive frames. As part of a preprocess, we decompose the surface of each polyhedron into convex pieces and construct bounding volume hierarchies to perform fast proximity queries. Once the objects have intersected, we compute the penetration depth (PD) in the neighborhood of the contact between each pair of decomposed convex pieces using a new incremental algorithm. Moreover, we cluster different contacts based on their spatial proximity to speed up the force computation. We have implemented this algorithm and applied it to complex contact scenarios consisting of multiple contacts. We demonstrate its effectiveness on electronic prototyping of complex mechanical structures and virtual exploration of a digestive system.