Minkowski sum boundary surfaces of 3D-objects

Abstract:

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.

Bibtex:

@article{peternell-2007-msb,
    author = {M. Peternell and T. Steiner},
    title = "{M}inkowski sum boundary surfaces of {3D}-objects",
    journal = {Graphical Models},
    year = {2007},
    volume=69,
        pages = "180-190",
}