我有三个三维点p1，p2和p3和球半径。如何找到球心从3点和半径？

我想到两个3D点作为解决方案，因为有2球是符合要求的。

感谢。

查找包含所有三个点的平面P。在这架飞机，这些 点确定一个三角形。

查找解决这个三角形的圈子。令C表示的中心 这个圈子。

查找线路垂直于P和位于C穿越它。

在这一行中，找到那些2点从理想的距离 圈子。

我忽略了退化情况。

I have three 3D points p1, p2 and p3 and the sphere radius. How do I find the sphere center from 3 points and radius?

I expect two 3D points as solution because there are 2 spheres that meet the requirements.

Thanks.

Find the plane P containing all three points. In that plane these points determine a triangle.

Find the circle around this triangle. Let C denote the center of this circle.

Find the line perpendicular to P and crossing it at C.

On this line, find those 2 points with the desired distance from the circle.

I have ignored degenerate cases.