Fast Distance Computation Using Quadratically Supported Surfaces

We use the class of surfaces with quadratic polynomial support functions in order to define bounding geometric primitives for shortest distance computation. The common normals of two such surfaces can be computed by solving a single polynomial equation of degree six. Based on this observation, we formulate an algorithm for computing the shortest distance between enclosures of two moving or static objects by surfaces of this type. It is demonstrated that the performance of this algorithm compares favourably with methods for computing the distance between two ellipsoids, which can also be used as bounding primitives for distance computation and collision detection.