FIMS: a New and Efficient Algorithm for the Computation of Minkowski Sum of Convex Polyhedra

The Minkowski sum computation and implementation in 2D and 3D domains is of a particular interest because it has a large number of applications in many domains such as: mathematical morphology, image processing and analysis, robotics, spatial planning, computer aided design and manufacturing, image processing ... However, no exact, fast, and general algorithms are found in the literature. We present in this paper a new and efficient algorithm based on a simple idea, for the calculation of the Minkowski sum of convex and closed polyhedra. Our implementation is general in the sense that it does not assume any constraint on the positions or the sizes of the polyhedra; it produces exact results and is faster than algorithms based on the convex hull computation. Our method can be easily generalized to an arbitrary dimensional space. We are also working on its adaptation to convex polyhedra which are not necessarily closed and for non-convex polyhedra without passing through the decomposition and union steps.