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We propose a generalised B-spline construction that extends uniform bi-degree B-splines to multisided regions spanned over extraordinary regions in quad-dominant meshes. We show how the structure of the existing cubic multisided B-spline patch can be generalised to work with B-spline basis functions of arbitrary degree and can be spanned over extraordinary vertices as well as extraordinary faces of quad-dominant meshes. The resulting multisided surfaces are Cd−1 continuous internally and connect with Gd−1 continuity to adjacent regular and other multisided B-splines patches. In addition, we design several specialised functions that increase the visual quality of the patches, in both the extraordinary vertex and face settings. CCS Concepts •Computing methodologies → Parametric curve and surface models;

Multisided B-spline Patches Over Extraordinary Regions