离非共面点最近的飞机？(Nearest plane to non-coplanar points?)

 我有许多非共面3D点，我想计算它们最近的平面（它们总是形成一个粗糙的平面，但有一些小的变化）。 这可以通过求解形式的每个点一个的联立线性方程来完成： 
 
 “Ax + By + Cz + D = 0” 
 
 我现在遇到的问题是双重的。 
 
 首先，因为点是3D浮点数，所以由于舍入误差，它们不能被精确地依赖。 
 
 其次，迄今为止我发现的所有以编程方式求解线性方程的方法都涉及使用NXN矩阵，这严重限制了我能够做的事情，因为我有4个未知数和任意数量的线性方程（由于数量的变化3D点数）。 
 
 有没有人有一个不错的方法来解决没有这些约束的联立线性方程，或者，更好的方法来计算最近的平面到非共面点？ （平面计算的精度不是太大关注） 
 
 谢谢！ :) 

I have a number of non-coplanar 3D points and I want to calculate the nearest plane to them (They will always form a rough plane but with some small level of variation). This can be done by solving simultaneous linear equations, one for each point, of the form:
 
"Ax + By + Cz + D = 0" 
 
The problem I'm having at the moment is twofold. 
 
Firstly since the points are 3D floats they can't be relied on to be precise due to rounding errors.
 
Secondly all of the methods to solving linear equations programatically that I have found thus far involve using NXN matrices which severely limits what I would be able to do given that I have 4 unknowns and any number of linear equations (due to the variation in the number of 3D points).
 
Does anyone have a decent way to either solve the simultaneous linear equations without these constraints or, alternatively, a better way to calculate the nearest plane to non-coplanar points? (The precision of the plane calculation is not too much of a concern)
 
Thanks! :)

原文：https://stackoverflow.com/questions/22743694