The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of "thick" facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
SUMMARYThe paper is concerned with the design and implementation of a parallel dynamic programming algorithm for use in ship voyage management. The basic concepts are presented in terms of a simple model for weather routing. Other factors involved in voyage management, and their inclusion in a more comprehensive algorithm, are also discussed. The algorithms have been developed and implemented using a transputer-based distributed-memory parallel machine using the high-level communication harness CS Tools. 'Ikial calculations over grids of up to 282 nodes have been carried out and the results are presented. Good speed-ups for the calculations have been attained, and the factors affecting the efficiency of the parallel computations are reviewed. These trial calculations indicate that a ship voyage management system based on parallal dynamic programming is likely to be beneficial.
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