Constant-time algorithms for constrained triangulations on reconfigurable meshes
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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/spl times/n. To the best of our knowledge, this is the first time constant time solutions to constrained triangulations are reported on this architecture.
Bokka, V. V., Gurla, H., Olariu, S., & Schwing, J. L. (1998). Constant-time algorithms for constrained triangulations on reconfigurable meshes. IEEE Transactions on Parallel and Distributed Systems, 9(11), 1057–1072. https://doi.org/10.1109/71.735954
IEEE Transactions on Parallel and Distributed Systems
Copyright © 1998, IEEE
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