Algorithms for laying points optimally on a plane and a circle

Two averaging algorithms are considered which are intended for choosing an optimal plane and an optimal circle approximating a group of points in three-dimensional Euclidean space.Comment: AmSTeX, 6 pages, amsppt styl

On linear regression in three-dimensional Euclidean space

The three-dimensional linear regression problem is a problem of finding a spacial straight line best fitting a group of points in three-dimensional Euclidean space. This problem is considered in the present paper and a solution to it is given in a coordinate-free form.Comment: AmSTeX, 4 pages, amsppt styl

On cylindrical regression in three-dimensional Euclidean space

The three-dimensional cylindrical regression problem is a problem of finding a cylinder best fitting a group of points in three-dimensional Euclidean space. The words best fitting are usually understood in the sense of the minimum root mean square deflection of the given points from a cylinder to be found. In this form the problem has no analytic solution. If one replaces the root mean square averaging by a certain biquadratic averaging, the resulting problem has an almost analytic solution. This solution is reproduced in the present paper in a coordinate-free form.Comment: AmSTeX, 10 pages, amsppt styl

ALGORITHMS FOR LAYING POINTS OPTIMALLY ON A PLANE AND A CIRCLE.

Abstract. Two averaging algorithms are considered which are intended for choosing an optimal plane and an optimal circle approximating a group of points in threedimensional Euclidean space. 1. Introduction. Assume that in the three-dimensional Euclidean space E we have a group of points visually resembling a circle (see Fig. 1.1). The problem is to find the best plane and the best circle approximating this group of points. Any plane in E i