Efficient structures for geometric data management
Efficient structures for geometric data management
V-Clip: fast and robust polyhedral collision detection
ACM Transactions on Graphics (TOG)
Penetration depth of two convex polytopes in 3D
Nordic Journal of Computing
Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space Expansion
IEEE Transactions on Visualization and Computer Graphics
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The directional contact range of two convex polyhedra is the range of positions that one of the polyhedra may locate in along a given straight line so that the two polyhedra are in collision. Using the contact range, one can quickly classify the positions along a line for a polyhedron as ''safe'' for free of collision with another polyhedron, or ''unsafe'' otherwise. This kind of contact detection between two objects is important in CAD, computer graphics and robotics applications. In this paper we propose a robust and efficient computation scheme to determine the directional contact range of two polyhedra. We consider the problem in its dual equivalence by studying the Minkowski difference of the two polyhedra under a duality transformation. The algorithm requires the construction of only a subset of the faces of the Minkowski difference, and resolves the directional range efficiently. It also computes the contact configurations when the boundaries of the polyhedra are in contact.