# A note on determining the 3-dimensional convex hull of a set of points on a mesh of processors

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## Abstract

This paper discusses the construction of the 3-dimensional convex hull for a set of n points stored on a √n × √n mesh of processors. Lu has shown that this problem can be solved in √n log n time if all points are located on a sphere. Here, we solve, in the same time-complexity, the 3-dimensional convex hull problem for arbitrary point sets. Furthermore, we observe a time/space trade off: if each processor is allocated O(log n) space then √n time is sufficient to determine the 3-dimensional convex hull.

## Keywords

Convex Hull Voronoi Diagram Tangent Plane Computational Geometry Storage Structure
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1988