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Robust Computation of Polyhedral Minkowski Sum Boundary  

Kyung, Min-Ho (Ajou University)
Sacks, Elisha (Purdue University)
Publication Information
Journal of the Korea Computer Graphics Society / v.16, no.2, 2010 , pp. 9-17 More about this Journal
Abstract
Minkowski sum of two polyedra is an operation to compute the sum of all pairs of points contained in the polyhedra. It has been a very useful tool to solve many geometric problems arising in the areas of robotics, NC machining, solid modeling, and so on. However, very few algorithms have been proposed to compute Minkowski sum of polyhedra, because computing Minkowski sum boundaries is susceptible to roundoff errors. We propose an algorithm to robustly compute the Minkowski sum boundaries by employing the controlled linear perturbation scheme to prevent numerically ambiguous and degenerate cases from occurring. According to our experiments, our algorithm computes the Minkowski sum boundaries with the precision of $10^{-14}$ by perturbing the vertices of the input polyhedra up to $10^{-10}$.
Keywords
Minkowski sum; triangle intersection; convolution;
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