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Computing the width of a set
September 1988 (vol. 10 no. 5)
pp. 761,762,763,764,765
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.<>

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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 and Machine Intelligence, vol. 10, no. 5, pp. 761,762,763,764,765, Sept. 1988, doi:10.1109/34.6790
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