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Constant-Time Algorithms for Constrained Triangulations on Reconfigurable Meshes
November 1998 (vol. 9 no. 11)
pp. 1057-1072

Abstract—A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconfigurable mesh has been proposed: In essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. The main contribution of this paper is to show that the flexibility of the reconfigurable mesh can be exploited for the purpose of obtaining constant-time algorithms for a number of constrained triangulation problems. These include triangulating a convex planar region containing any constant number of convex holes, triangulating a convex planar region in the presence of a collection of rectangular holes, and triangulating a set of ordered line segments. Specifically, with a collection of O(n) such objects as input, our algorithms run in O(1) time on a reconfigurable mesh of size n×n. To the best of our knowledge, this is the first time constant time solutions to constrained triangulations are reported on this architecture.

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Index Terms:
Computer-aided manufacturing, robotics, CAD, VLSI design, computer-aided geometric design, constrained triangulations, reconfigurable meshes, constant time algorithms.
Citation:
VenkataVasu Bokka, Himabindu Gurla, Stephan Olariu, James L. Schwing, "Constant-Time Algorithms for Constrained Triangulations on Reconfigurable Meshes," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 11, pp. 1057-1072, Nov. 1998, doi:10.1109/71.735954
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