我如何解决球体中心 [英] How do I solve centre of sphere

问题描述

我们知道球体和半径上两点的坐标，如何得到中心的坐标？

谢谢！

解决方案

请参阅我对PIEBALDconsult对该问题的评论的评论。想象一下：

 p1 p2 
 \ / 
r \ / r 
 \ / 
 \ / 
 center 
 

当您拥有连续的解决方案时，这就是中心位置的一般情况。显然，半径为r的球体的中心位于围绕每个点的球体上，p1作为中心，或p2作为中心。两个球体相交形成一个圆（垂直于我的绘图平面，中心对称地位于p1和p2之间）。这个圆圈的每个点都是一个解决方案。



如果p1和p2之间的距离恰好是2 * r，那么你只有一个解决方案：

 p1 p2 
 ------------ + ------------ 
 center 
rr 

最后，如果p1和p2之间的距离大于2 * r，则没有解决方案。



这是高中几何学的一个基本问题，实际上是偏离主题的。

-SA

对于球体，只需知道其表面的两个坐标及其半径 - 无法获得其中心的坐标。



即使圈获得其中心的坐标 - 我们的圆周上至少需要三个点。如果你只知道两个圆周点和圆的半径 - 那么将有两个可能的圆与该数据。请看下面的链接：

http://mathforum.org/library/ drmath / view / 54490.html [ ^ ]



要计算球体的中心，你需要至少四个点，更具体地说至少需要四个非共面点，并且包含三个非共线点的。这里有相同的讨论：

http://steve.hollasch.net/ cgindex / geometry / sphere4pts.html [ ^ ]



希望这会有所帮助。感谢。

We know that coordinates of two points on sphere and radius ,how to get coordinate of centre ?
thank you!

解决方案

Please see my comment to the comment to the question by PIEBALDconsult. Picture this:

 p1      p2
 \      /
r \    / r
   \  /
    \/
     center

This is how the location of the center looks in general case, when you have the continuum of solutions. Apparently, the center of the sphere of radius r lies on the sphere surrounding each of the points, p1 as a center, or p2 as a center. The two spheres intersect forming a circle (perpendicular to the plane of my drawing, with the center which lies symmetrically between p1 and p2). Each point of this circle is a solution.

If the distance between p1 and p2 is exactly 2*r, you have only one solution:

p1                       p2
------------+------------
          center 
     r              r

Finally, if the distance between p1 and p2 is greater that 2*r, there are no solutions.

This is an elementary problem on high-school geometry, in fact, off-topic.

—SA

For a sphere, just by knowing two coordinates of its surface and its radius - getting coordinate of its center is not possible.

Even for circle to get the coordinate of its center - we need at least three points on its circumference. and if you just know two points of circumference and radius of circle - there would be two possible circles with that data. Please have a look on below link:
http://mathforum.org/library/drmath/view/54490.html[^]

To figure out center of a sphere, you need at least four points, more specifically at least four noncoplanar points, and contains three noncollinear points . There is discussion about the same here:
http://steve.hollasch.net/cgindex/geometry/sphere4pts.html[^]

Hope this will help. Thanks.

这篇关于我如何解决球体中心的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！