A fast geometric algorithm for finding the minimum distance between two convex hulls

The problem of computing the minimum distance between two convex hulls has applications to many areas including robotics, computer graphics, path planning, and data classification. In this paper, we propose and investigate a new algorithm (based on the MDM algorithm) for finding the minimum distance between two convex hulls. The new algorithm is simple to understand and easy to implement. The convergence of the algorithm is proved and the performance of the algorithm is compared with the state-of-art techniques. For randomly generated data sets, the new algorithm is more efficient than some of the best available algorithms and implementations, in particular when the number of points and the dimensions are large.