Minkowski sum boundary surfaces of 3D-objects

Given two solids A and B with piecewise smooth boundary we discuss the computation of the boundary Γ of the Minkowski sum A + B. This boundary surface Γ is part of the envelope when B is moved by translations defined by vectors a ∈ A, or vice versa. We present an efficient algorithm working for dense point clouds or for triangular meshes. Besides this, the global self intersections of the boundary Γ are detected and resolved. Additionally we point to some relations between Minkowski sums and kinematics, and compute local quadratic approximations of the envelope. keywords: Minkowski sum, convolution surface, translation, motion, envelope, marching algorithm, point-set surface, signed distance function.