MU Faculty of Informatics Masaryk University Lower Bound of Distance in 3 D by Petr

The term “collision detection” refers to the task of determining whether, in a given set of objects, any two intersect. If they do, then common collision detection systems return either one such pair or all such pairs. The term “proximity computation” refers to a more general task where we determine the nearest or the “most overlapping” pairs of objects. In the article, we present a new method to rapidly compute lower bounds of distances. The lower bound decreases the complexity of collision detection (or proximity computation) by computing “candidates” of collision, i.e., pairs of objects that might intersect. It estimates the lower bound of their distance and rejects pairs that are too far from each other to collide. 1 Collision detection Detection of collisions between virtual objects is one of the basic tasks in virtual reality type of applications. For instance, a program that maintains a virtual body (“avatar”) in a virtual environment often depends critically on knowing when and where the avatar collides with the environment. Similarly, a modern CAD system must be able to check if the given model satisfies engineering constraints, such as the required separation of the hydraulic systems of an aircraft from the aircraft’s moving parts. Computations of lower bounds of distances between objects are used to ensure separations and to detect or eliminate collisions. Clearly, a trivial method of finding a distance bound between two objects is to compute the exact distances between all pairs of relevant (convex) subregions; then the minimum of these distances is the best lower bound possible. However, such a brute force approach is too time consuming to Fulbright Visiting Professor (on leave from The Boeing Company), Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic, [email protected] Student, Masaryk University, [email protected]