Hettinga, Gerben J.Kosinka, JiriBiasotti, Silvia and Pintus, Ruggero and Berretti, Stefano2020-11-122020-11-122020978-3-03868-124-32617-4855https://doi.org/10.2312/stag.20201235https://diglib.eg.org:443/handle/10.2312/stag20201235We 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.Computing methodologiesParametric curve and surface models10.2312/stag.202012359-17