寻找最小边界球为截锥体 [英] Finding a minimum bounding sphere for a frustum

问题描述

我有截锥体（棱锥），我需要计算一个边界球为这个视锥那是尽可能小。我可以选择中间是正确的视锥和半径的中心是远的一个角落的距离，但是，通常留下了不少松弛周围的圆台的窄端

I have a frustum (truncated pyramid) and I need to compute a bounding sphere for this frustum that's as small as possible. I can choose the centre to be right in the centre of the frustum and the radius be the distance to one of the "far" corners, but that usually leaves quite a lot of slack around the narrow end of the frustum

这似乎是简单的几何体，但我似乎无法弄清楚。任何想法？

This seems like simple geometry, but I can't seem to figure it out. Any ideas?

推荐答案

嗯，有<一href="http://www.cgafaq.info/wiki/Minimal_enclosing_sphere">http://www.cgafaq.info/wiki/Minimal_enclosing_sphere当然（通过谷歌）。

Well, there's http://www.cgafaq.info/wiki/Minimal_enclosing_sphere of course (via Google).

我倒是觉得有两种可能。酮（如平截头体是非常平的）是，该碱的相对点成为球体上的相对点。其他（如平截头体是非常高），将是，截头锥体的相对点是在球体上，你会找出不同于四个点的球体（1点的基础上，1相对的第一底座上， 1对面第一个较高的广场上，一个相邻的第一个较高广场）。

I'd think there are two possibilities. One (if the frustum is very flat) would be that the opposite points of the base become opposite points on the sphere. The other (if the frustum is very tall) would be that opposite points of the frustum would be on the sphere and you'd figure out the sphere from those four points (one point on the base, one opposite the first on the base, one opposite the first on the higher square, one adjacent the first on the higher square).

图出第一球。如果视锥在它适合，这就是你的答案。否则，第二球是你的答案。

Figure out the first sphere. If the frustum fits in it, that's your answer. Otherwise, the second sphere would be your answer.

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