Issue No. 05 - September (1988 vol. 10)

ISSN: 0162-8828

pp: 761,762,763,764,765

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.6790

ABSTRACT

For a set of points P in three-dimensional space, the width of P, W (P), is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n log n+I) time and O(n) space, where I is the number of antipodal pairs of edges of the convex hull of P, and n is the number of vertices; in the worst case, I=O(n/sup 2/). For a convex polyhedra the time complexity becomes O(n+I). If P is a set of points in the plane, the complexity can be reduced to O(nlog n). For simple polygons, linear time suffices.<>

INDEX TERMS

set theory, computational complexity, computational geometry, pattern recognition, polygons, 3D space, point sets, computational complexity, pattern recognition, computational geometry, parallel planes, convex hull, time complexity, Concurrent computing, Artificial intelligence, Computational geometry, Image processing, Minimax techniques, Pattern recognition, Canada Councils, Computer science, Terminology, Euclidean distance

CITATION

"Computing the width of a set",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 10, no. , pp. 761,762,763,764,765, September 1988, doi:10.1109/34.6790