A distance hierarchy to detect collisions between deformable objects

To detect collisions between deformable objects we introduce an algorithm that computes the closest distances between certain feature points defined in their meshes. The strategy is to divide the objects into regions and to define a representative vertex that serves to compute the distance to the regions of the other objects. Having obtained the closest regions between two objects, we proceed to explore these regions by expanding them and detecting the closest sub-regions. We handle a hierarchy of regions and distances where the first level contains n1 regions, each one is divided into n2 sub-regions, and so on. A collision is obtained when the distance between two vertices in the last level of the tree is less than a predefined value e. The advantage of our algorithm is that we can follow the deformation of the surface with the representative vertices defined in the hierarchy.