Collisional detection is an algorithmic problem, which is dealt by all areas of computer science related to the simulation of physical objects in motion. Collision detection algorithms can be classified in various ways, from the geometric object model, to theoretical concerns such as worst-case complexity. Two algorithms for a precise collision detection between two potentially colliding objects are presented in this article, among which the first one uses axis-aligned bounding boxes (AABB) and is a typical representative of a computational geometry algorithm, while the second one uses spherical distance fields originating in image processing. The AABB-based algorithm uses discrete structures to achieve the necessary refinement, whereas the distance field based algorithm uses a refinement strategy known from signal processing. The two collision detection algorithms are also suitable for all model types including polygon soups, surfaces or volumetric models.