Intersection of convex objects in two and three dimensions

Author:

Chazelle B.1,Dobkin D. P.2

Affiliation:

1. Yale Univ., New Haven, CT

2. Princeton Univ., Princeton, NJ

Abstract

One of the basic geometric operations involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output. For many applications, however, it may be assumed that the objects already exist within the computer and that the only output desired is a single piece of data giving a common point if the objects intersect or reporting no intersection if they are disjoint. For this problem, none of the previous lower bounds are valid and algorithms are proposed requiring sublinear time for their solution in two and three dimensions.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Reference17 articles.

1. Algorithms for reporting and counting geometric intersections;BENTLEY J. L.;IEEE Trans. Comput. C-28,1979

2. Divide and conquer for linear expected time;BENTLEY L.;Inf. Proc. Lett.,1978

3. Fast detection of polyhedral intersection;DOBKIN D. P.;Theor. Comput. Sci.,1983

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