我在寻找一种算法来找到一个点云和球体之间的最佳契合。

也就是说，我希望尽量减少

其中的 C 的是球体的中心，研究的半径，并且每个的 P 的在我的组的一个点n 的点。这些变量明显的 CX 的赛扬的锆石和研究的。 就我而言，我可以得到一个已知的研究的事前，留下的 C 的只是组件的变量。

我真的不希望有使用任何一种迭代的最小化（如牛顿法，列文伯格 - 马夸特等） - 我倒是preFER一组线性方程组或明确的解决方案使用SVD 解决方案

有没有矩阵方程即将到来。您所选择的E是非常表现;它的偏导数甚至不连续的，更何况是线性的。即使有不同的目标，这个优化问题似乎从根本上非凸;与一个点P和非零半径r，该组最优解的是约P上的球体。

您或许应该reask上有更多的优化知识的交流。

I'm looking for an algorithm to find the best fit between a cloud of points and a sphere.

That is, I want to minimise

where C is the centre of the sphere, r its radius, and each P a point in my set of n points. The variables are obviously Cx, Cy, Cz, and r. In my case, I can obtain a known r beforehand, leaving only the components of C as variables.

I really don't want to have to use any kind of iterative minimisation (e.g. Newton's method, Levenberg-Marquardt, etc) - I'd prefer a set of linear equations or a solution explicitly using SVD.

There are no matrix equations forthcoming. Your choice of E is badly behaved; its partial derivatives are not even continuous, let alone linear. Even with a different objective, this optimization problem seems fundamentally non-convex; with one point P and a nonzero radius r, the set of optimal solutions is the sphere about P.

You should probably reask on an exchange with more optimization knowledge.