# On cylindrical regression in three-dimensional Euclidean space

## TL;DR

This paper addresses the problem of fitting a cylinder to 3D data points, proposing an almost analytic solution using biquadratic averaging that simplifies the traditionally complex problem.

## Contribution

It introduces a coordinate-free, near-analytic solution to the 3D cylindrical regression problem using biquadratic averaging.

## Key findings

- Provides an almost analytic solution to cylindrical regression
- Reproduces the solution in a coordinate-free form
- Simplifies the fitting process compared to traditional methods

## Abstract

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.