Abstract

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 ellipsoid-and 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.

We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non-linear systems. By exploring the direct relationship between a standard higher-order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve-based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.

An increasing number of projects have examined the perceptual magnitude of visible artifacts in animated motion