A multisided C-2 B-spline patch over extraordinary vertices in quadrilateral meshes

We propose a generalised B-spline construction that extends uniform bicubic B-splines to multisided regions spanned over extraordinary vertices in quadrilateral meshes. We show how the structure of the generalised Bezier patch introduced by Varady et al. can be adjusted to work with B-spline basis functions. We create ribbon surfaces based on B-splines using special basis functions. The resulting multisided surfaces are C-2 continuous internally and connect with G(2) continuity to adjacent regular and other multisided B-splines patches. We visually assess the quality of these surfaces and compare them to Catmull-Clark limit surfaces on several challenging geometrical configurations. (C) 2020 The Author(s). Published by Elsevier Ltd.