Computational geometry: an introduction
Computational geometry: an introduction
An O(log n) time parallel algorithm for triangulating a set of points in the plane
Information Processing Letters
Mesh Computer Algorithms for Computational Geometry
IEEE Transactions on Computers
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Parallel computational geometry
Parallel computational geometry
Optimal Parallel Algorithms for Finding Proximate Points, with Applications
IEEE Transactions on Parallel and Distributed Systems
Constructing the constrained Delaunay triangulation on the Intel paragon
SAC '97 Proceedings of the 1997 ACM symposium on Applied computing
| Hi-index | 0.00 |
In this paper, we present some efficient parallel geometric algorithms for computing the All Nearest Neighbors, Delaunay Triangulation, Convex Hull, and Voronoi Diagram of a point set S with N points in the plane. The algorithm of All Nearest Neighbors is to find the nearest-neighbor point for each point in S. It can be applied to cluster analysis, classification theory and computational geometry. A Delaunay Triangulation of S is an triangulation in which the circumcircle of each triangle contains no any other point of S. Delaunay Triangulation has practical applications on finite-element method, computational fluid dynamics, geometric modeling, visualization, numerical analysis, and computational geometry. The Convex Hull of S is the smallest convex polygon that includes all the points of S. Convex hull has many applications in pattern recognition, image processing, stock cutting and allocation, and computational geometry. The straight-line dual of a Voronoi Diagram is a Delaunay Triangulation. Voronoi Diagram is a very useful data structure for robotics, image processing, graph theory, computational fluid dynamics, and computational geometry. We use a mesh of trees with N × N processors as the computation model. All of these parallel algorithms have the same good time complexity O (log N) [1][9].