Extraction of cylinders and cones from minimal point sets

•Extraction of the right cylinders passing through three 3D points, one of them being oriented.•Extraction of the right cylinders passing through five 3D points.•Extraction of the right circular cones passing through two oriented 3D points.•Extraction of the right circular cones passing through four 3D points, one of them being oriented.•Extraction of the right circular cones passing through six 3D points. [Display omitted] 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.