Corner-Based Implicit Patches

Free-form multi-sided surfaces are often defined by side interpolants (also called ribbons), requiring that the surface has to connect to them with a prescribed degree of smoothness. I-patches represent a family of implicit surfaces defined by an arbitrary number of ribbons. While in the case of parametric surfaces describing ribbons is a well-discussed problem, defining implicit ribbons is a different task. In this paper, we introduce a new representation, corner I-patches, where implicit corner interpolants are blended together. Corner interpolants are usually simpler, lower-degree surfaces than ribbons. The shape of the patch depends on a handful of scalar parameters; constraining them ensures continuity between adjacent patches. Corner I-patches have several favorable properties that can be exploited for design, volume rendering, or cell-based approximation of complex shapes.