Corner-based implicit patches

TL;DR

This paper introduces corner I-patches, a new implicit surface representation based on corner interpolants, which simplifies shape definition and enforces continuity through scalar parameters, benefiting applications like volume rendering and approximation.

Contribution

The paper presents corner I-patches, a novel implicit surface model that simplifies shape control and continuity enforcement compared to existing multi-sided surface representations.

Findings

Corner I-patches are defined with simple surfaces and scalar parameters.

Continuity between patches is enforced via parameter constraints.

The approach has advantages in volume rendering and surface approximation.

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.