Collision Detection for Moving Polyhedra
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Precise global collision detection in multi-axis NC-machining
Computer-Aided Design
Precise global collision detection in multi-axis NC-machining
Computer-Aided Design
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We introduce a new approach to the problem of collision detection between a rotating milling-cutter of an NC-machine and a model of a solid workpiece, as the rotating cutter continuously moves near the workpiece. Having five degrees of motion freedom, this problem is hard to solve exactly and we approximate the motion of the tool by a sequence of sub-paths of pure translations interleaved with pure rotations. The detection problem along each sub-path is then solved by using radial projection of the obstacles (the workpiece and other parts of the NC-machine) around the tool axis to obtain a collection of critical surface patches in ℝ3, and by examining planar silhouettes of these surface patches. We thus reduce the problem to successive computations of the lower envelope of a set of planar curves --- this reduction is exact, and incurs no loss of accuracy. We have implemented our algorithm in the IRIT environment for solid modeling, using an extension package of the CGAL library for computing envelopes. The algorithm, combined with the proper data structures, solves the collision detection problem in a robust manner, yet it yields efficient computation times as our experiments show. Our approach produces exact results in case of purely translational motion, and provides guaranteed (and good) approximation bounds in case the motion includes rotation.