Lower bound of distance in 3D

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