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Largest empty sphere
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Largest empty sphere : ウィキペディア英語版
Largest empty sphere

In computational geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in ''d''-dimensional space whose interior does not overlap with any given obstacles.
==Two dimensions==
The largest empty circle problem is the problem of finding a circle of largest radius in the plane whose interior does not overlap with any given obstacles.
A common special case is as follows. Given ''n'' points in the plane, find a largest circle centered within their convex hull and enclosing none of them. The problem may be solved using Voronoi diagrams in optimal time \Theta(n\, \log\, n).〔G. T. Toussaint, "Computing largest empty circles with location constraints," ''International Journal of Computer and Information Sciences'', vol. 12, No. 5, October, 1983, pp. 347-358.〕
==See also==

*Bounding sphere
*Farthest-first traversal
*Largest empty rectangle

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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