Type-Constrained Direct Fitting of Quadric Surfaces

We present a catalog of type-specific, direct quadric fitting methods: Given a selection of a point cloud or triangle mesh, and a desired quadric type (e.g. cone, ellipsoid, paraboloid, etc), our methods recover a best-fit surface of the given type to the given data. Type-specific quadric fitting methods are scattered throughout the literature; here we present a thorough, practical collection in one place. We add new methods to handle neglected quadric types, such as non-circular cones and general rotationally symmetric quadrics. We improve upon existing methods for ellipsoidand hyperboloid-specific fitting. Our catalog handles a wide range of quadric types with just two high-level fitting strategies, making it simpler to understand and implement.