Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
On the detection of a common intersection of k convex objects in the plane
Information Processing Letters
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
On the computational geometry of pocket machining
On the computational geometry of pocket machining
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Range searching with efficient hierarchical cuttings
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Feasability of Design in Stereolithography
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Separating an object from its cast
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Casting with Skewed Ejection Direction
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
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A polyhedron P is castable if its boundary can be partitioned by a plane into two polyhedral terrains. Such polyhedra can be manufactured easily using two cast parts. Assuming that the cast parts are removed by a single translation each, it is shown that for a simple polyhedron with n vertices, castability can be decided in O(n2logn) time and linear space using a simple algorithm. Furthermore, a more complicated algorithm solves the problem in O(n3/2+&egr;) time and space, for any fixed &egr;0. In the case where the cast parts are to be removed in opposite directions, a simple O(n2) time algorithm is presented. Finally, if the object is a convex polyhedron and the cast parts are to be removed in opposite directions, a simple O(nlog2n) algorithm is presented.