Robust Minkowski sums of polyhedra via controlled linear perturbation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A GPU-based voxelization approach to 3D Minkowski sum computation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Motion planning via manifold samples
ESA'11 Proceedings of the 19th European conference on Algorithms
PolyDepth: Real-time penetration depth computation using iterative contact-space projection
ACM Transactions on Graphics (TOG)
Controlled linear perturbation
Computer-Aided Design
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Computer-Aided Design
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
ACM Transactions on Graphics (TOG)
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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We present the first exact and robust implementation of the 3D Minkowski sum of two non-convex polyhedra. Our implementation decomposes the two polyhedra into convex pieces, performs pairwise Minkowski sums on the convex pieces, and constructs their union. We achieve exactness and the handling of all degeneracies by building upon 3D Nef polyhedra as provided by Cgal. The implementation also supports open and closed polyhedra. This allows the handling of degenerate scenarios like the tight passage problem in robot motion planning. The bottleneck of our approach is the union step. We address efficiency by optimizing this step by two means: we implement an efficient decomposition that yields a small number of convex pieces, and develop, test and optimize multiple strategies for uniting the partial sums by consecutive binary union operations. The decomposition that we implemented as part of the Minkowski sum is interesting in its own right. It is the first robust implementation of a decomposition of polyhedra into convex pieces that yields at most O(r 2) pieces, where r is the number of edges whose adjacent facets comprise an angle of more than 180 degrees with respect to the interior of the polyhedron.