Corner-based implicit patches

Abstract: Multi-sided surfaces are often defined by side interpolants (also called ribbons), i.e. the surface has to connect to the ribbons with a prescribed degree of smoothness. The I-patch is such a family of implicit surfaces capable of interpolating an arbitrary number of ribbons and can be used in design and approximation. While in the case of parametric surfaces describing ribbons is a well-discussed problem, defining implicit ribbons is a different task. This paper will introduce corner I-patches, a new representation that describes implicit surfaces based on corner interpolants. Those may be defined with much simpler surfaces, while the shape of the patch will depend on a handful of scalar parameters. Continuity between patches will be enforced via constraints on these parameters. Corner I-patches have several favorable properties that can be exploited for example in volume rendering or approximation.