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Computing the width of a set

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2 Author(s)
Houle, M.E. ; Sch. of Comput. Sci., McGill Univ., Montreal, Que., Canada ; Toussaint, G.T.

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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:10 ,  Issue: 5 )