Extraction of cylinders and cones from minimal point sets

TL;DR

This paper introduces algebraic methods for efficiently extracting cylinders and cones from minimal point sets, including oriented points, with optimal bounds on solutions for various interpolation problems.

Contribution

It provides new algebraic techniques and bounds for extracting cylinders and cones from minimal point configurations, improving computational efficiency.

Findings

Optimal bounds on the number of solutions for each problem

Efficient algebraic methods for shape extraction

Applicable to minimal point sets with orientations

Abstract

We propose new algebraic methods for extracting cylinders and cones from minimal point sets, including oriented points. More precisely, we are interested in computing efficiently cylinders through a set of three points, one of them being oriented, or through a set of five simple points. We are also interested in computing efficiently cones through a set of two oriented points, through a set of four points, one of them being oriented, or through a set of six points. For these different interpolation problems, we give optimal bounds on the number of solutions. Moreover, we describe algebraic methods targeted to solve these problems efficiently.