Multi-sided B-spline surfaces over curved, multi-connected domains

We propose a new surface representation, the Generalized B-spline (GBS) patch, that combines ribbon interpolants given in B-spline form. A GBS patch can connect to tensor-product B-spline surfaces with arbitrary G(m) continuity. It supports ribbons not only along the perimeter loop, but also around holes in the interior of the patches. This is a follow-up paper of a recent publication(Varady et al., 2020) that described multi-sided Bezier surfaces over curved multi-sided domains. While the fundamental concept is retained, several new details have been elaborated. The weighting functions are modified to be products of B-spline and Bernstein basis functions, multiplied by rational terms. A new local parameterization method is introduced using harmonic functions, that handles periodic hole loops, as well. Interior shape control is adapted to the B-spline representation of the ribbons. Several examples illustrate the capabilities of the proposed scheme. Our implementation is based on a computationally efficient discretization. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

The paper introduces a new surface representation called Generalized B-spline (GBS) patch that combines ribbon interpolants in B-spline form and connects to tensor-product B-spline surfaces with arbitrary G(m) continuity. It elaborates on new details such as modified weighting functions and introduces a new local parameterization method using harmonic functions to handle periodic hole loops. Several examples illustrate the capabilities of the proposed scheme, which is based on a computationally efficient discretization.