Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Computational geometry.
Geometric transforms for fast geometric algorithms
Geometric transforms for fast geometric algorithms
Planar geometric location problems and maintaining the width of a planar set
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Diameter, width, closest line pair, and parametric searching
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Computing envelopes in four dimensions with applications
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Podality-Based Time-Optimal Computations on Enhanced Meshes
IEEE Transactions on Parallel and Distributed Systems
The Mesh with Hybrid Buses: An Efficient Parallel Architecture for Digital Geometry
IEEE Transactions on Parallel and Distributed Systems
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus
Proceedings of the sixteenth annual symposium on Computational geometry
On some geometric selection and optimization problems via sorted matrices
Computational Geometry: Theory and Applications
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Given a set of points P = {p1,p2,…,pn} in three dimensions, 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 &Ogr;(n log n + I) time and &Ogr;(n) space, where I is the number of antipodal pairs of edges of the convex hull of P, and in the worst case I - &Ogr;(n2). If P is a set of points in the plane, this complexity can be reduced to &Ogr;(n log n). Finally, for simple polygons linear time suffices.