Covering Minkowski sum boundary using points with applications
Computer Aided Geometric Design
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
Planning motion in point-represented contact spaces using approximate star-shaped decomposition
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Uniform offsetting of polygonal model based on Layered Depth-Normal Images
Computer-Aided Design
Contributing vertices-based Minkowski sum of a nonconvex--convex pair of polyhedra
ACM Transactions on Graphics (TOG)
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Minkowski sum is a fundamental operation in many geometric applications, including robotics, penetration depth estimation, solid modeling, and virtual prototyping. However, due to its high computational complexity and several nontrivial implementation issues, computing the exact boundary of the Minkowski sum of two arbitrary polyhedra is generally a difficult task. In this work, we propose to represent the boundary of the Minkowski sum approximately using only points. Our results show that this point-based representation can be generated efficiently. An important feature of our method is its straightforward implementation and parallelization. We also demonstrate that the point-based representation of the Minkowski sum boundary can indeed provide similar functionality as meshbased representations can. We show several applications in motion planning, penetration depth approximation and modeling. An implementation of the proposed method can be obtained from our project webpage at: http://www.cs.gmu.edu/~jmlien/mksum/