Tracking minimum distances between curved objects with parametric surfaces in real time

This paper presents a new algorithm for real-time tracking of pairs of closest points as well as their corresponding surface features between certain general types of objects (which can be non-convex) with parametric curved surfaces. The fact that the algorithm works directly on accurate parametric descriptions of curved surfaces rather than polygonal approximation of surfaces (i.e., polygonal meshes) enables it to not only provide accurate collision detection among certain curved objects in real-time, but more importantly, also provide accurate description of the state of a collision, i.e., the actual regions of contact in real-time. Such capability is very useful in applications requiring high accuracy in real-time, including certain haptic rendering tasks for virtual prototyping or virtual training. Test results show that the algorithm achieves correct tracking in the rate of 1 kHz.