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Minimum bounding box algorithms
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Minimum bounding box algorithms : ウィキペディア英語版
Minimum bounding box algorithms
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, ''etc.'' of the box.
It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is straightforward to find the smallest enclosing box that has sides parallel to the coordinate axes; the difficult part of the problem is to determine the orientation of the box.
==Two dimensions==
For the convex polygon, a linear time algorithm for the minimum-area enclosing rectangle is known. It is based on the observation that a side of a minimum-area enclosing box must be collinear with a side of the convex polygon.〔.〕 It is possible to enumerate boxes of this kind in linear time with the approach called rotating calipers by
Godfried Toussaint in 1983.〔.〕 The same approach is applicable for finding the minimum-perimeter enclosing 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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