New upper bounds in Klee's measure problem
SIAM Journal on Computing
Introduction to Algorithms
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Computing the volume of the union of cubes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Five-axis tool path generation for a flat-end tool based on iso-conic partitioning
Computer-Aided Design
Free-Form Surface Partition in 3-D
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Image Segmentation with Monotonicity and Smoothness Constraints
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Data structures for range minimum queries in multidimensional arrays
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms for interval structures with applications
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Algorithms for interval structures with applications
Theoretical Computer Science
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We present several algorithms for computing a feasible tool-path with desired features for sculpting a given surface using a 5-axis numerically controlled (NC) machine in computer-aided manufacturing. A toolpath specifies the orientation of a cutting tool at each point of a path taken by the tool. Previous algorithms are all heuristics with no quality guarantee of solutions and with no analysis of the running time. We present optimal quality solutions and provide time analysis for our algorithms. We model the problems using a directed, layered graph G such that a feasible toolpath corresponds to a certain path in G, and give efficient methods for solving several path problems in such graphs.