#### Topic: To find the plane equation minimum remote from a cloud.

There is a cloud of points in 3D. It is necessary to find the plane equation the total distance from which to all points would be minimum. There is a pair of ideas how to make, but  who offers that? Or can eat generally  on computing geometry. But it is not interesting, it would be desirable variants of algorithms .

#### Re: To find the plane equation minimum remote from a cloud.

Hello, SergeyOsipov, you wrote: SO> There is a cloud of points in 3D. It is necessary to find the plane equation the total distance from which to all points would be minimum. There is a pair of ideas how to make, but  who offers that? Or can eat generally  on computing geometry. But it is not interesting, it would be desirable variants of algorithms . Sounds as normal linear approximation. Well and the least-squares method occurs at once...

#### Re: To find the plane equation minimum remote from a cloud.

Hello, SergeyOsipov, you wrote: SO> There is a cloud of points in 3D. It is necessary to find the plane equation the total distance from which to all points would be minimum. There is a pair of ideas how to make, but  who offers that? Or can eat generally  on computing geometry. But it is not interesting, it would be desirable variants of algorithms . Whether the least-squares method which minimizes the total of squares of orthogonal distances to a plane approaches? And if preferential orientation of a cloud it is possible also distances along any axis is known to optimize (it easier, dares system from three linear equations of a type with members of type Sum (xi^2), Sum (xi*yi) etc., and in the first case how much I remember, it is necessary to search for own numbers of a matrix)

#### Re: To find the plane equation minimum remote from a cloud.

Hello, SergeyOsipov, you wrote: SO> There is a cloud of points in 3D. It is necessary to find the plane equation the total distance from which to all points would be minimum. There is a pair of ideas how to make, but  who offers that? Or can eat generally  on computing geometry. But it is not interesting, it would be desirable variants of algorithms . PCA from which result to take the two first vector through which to lead a plane.

#### Re: To find the plane equation minimum remote from a cloud.

Hello, SergeyOsipov, you wrote: SO> There is a cloud of points in 3D. It is necessary to find the plane equation the total distance from which to all points would be minimum. There is a pair of ideas how to make, but  who offers that? Or can eat generally  on computing geometry. But it is not interesting, it would be desirable variants of algorithms . 1) If I truly understood your task it is possible to state that the required plane transits through center of masses of all points. That is it is a question of selection of a corner of a normal to a plane. We receive the two-dimensional task of optimization. Whether enough the suboptimal decision? If the cloud of points has any simple structure (we tell the Gauss with different a sigma in different directions) the simple method of conjugate gradients gives an extremum. 2) if the cloud has difficult structure there can be many local maxima. I think that well will be shown by diff. Evolution. The only thing that it is possible to make a vector 3D, simply to normalize their length on each step. Well and  it is possible not swap of coordinates, and the linear operations over vectors. Yours faithfully, E.

#### Re: To find the plane equation minimum remote from a cloud.

Hello, Erop, you wrote: E> 1) If I truly understood your task it is possible to state that the required plane transits through center of masses of all points. Actually this plane for the decision of this task - http://rsdn.org/forum/life/6826966.1 the Author was necessary to me: SergeyOsipov Date: 01.07 09:12 Simply any more did not know as to solve, and wanted to adjust somehow the data to the answer and to average. But it was not required, an error there found so to average values it is not necessary any more. But all the same all thanks.