Video: Exact Minkowski sums of convex polyhedra

We present an exact implementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R 3. Our implementation is complete in the sense that it does not assume general position, namely, it can handle degenerate input, and produces exact results. Our software also includes applications of the Minkowski-sum computation to answer collision and proximity queries about the relative placement of two convex polyhedra in R 3. The algorithms use a dual representation of convex polyhedra, and their implementation is mainly based on the Arrangement package of Cgal, the Computational Geometry Algorithm Library. We compare our Minkowski-sum construction with a naïve approach that computes the convex hull of the pairwise sums of vertices of two convex polyhedra. Our method is significantly faster. The video demonstrates the techniques used on simple cases as well as on degenerate cases. The relevant programs, source code, data sets, and documentation are available a