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• W1973592371 abstract "Abstract Let P = P 1 , P 2 , …, P m be a set of m convex polygons in the plane with a total number of n vertices, and for 1 ⩽ i ⩽ m , let w i gE R + be a weight associated with P i . The weighted distance between a line l and a polygon P i is given by d ( l , P i ) = min pϵP i , qϵl d ( p , q ). w i , where d ( p , q ) is the Euclidean distance between p and q . We want to compute a line l that minimizes the maximum distance between l and the polygons of P . We present an O( nα ( n ) log 3 n )-time algorithm to compute such a line. We also give an O( n 2+ e )-time algorithm, where e is an arbitrarily small positive constant, to solve the three dimensional version of this problem; here, P is a set of convex polytopes in R 3 , and we want to compute a plane h that minimizes the maximum weighted distance between h and the polytopes." @default.
• W1973592371 created "2016-06-24" @default.
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• W1973592371 date "1997-04-01" @default.
• W1973592371 modified "2023-09-25" @default.
• W1973592371 title "Linear approximation of simple objects" @default.
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• W1973592371 doi "https://doi.org/10.1016/s0020-0190(97)00049-5" @default.
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