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.
Peternell et al. REF proposed a method to compute the Minkowski sum of two solids using points densely sampled from the solids, and compute local quadratic approximations of these points.
Minkowski sum boundary surfaces of 3D-objects
Vienna Univ
Computer Science Mathematics