Minkowski sum boundary surfaces of 3D-objects |
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| Authors: | Martin Peternell Tibor Steiner |
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| Affiliation: | aInstitute of Discrete Mathematics and Geometry, University of Technology Vienna, Wiedner Hauptstraße 8–10, 1040 Wien, Austria |
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| Abstract: | Given two objects 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. |
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| Keywords: | Minkowski sum Convolution surface Translation Motion Envelope Marching algorithm Point set surface Signed distance function |
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