Localized G-splines for quad & T-gon meshes

Enriching tensor-product B-spline control nets by allowing T-gons (where strips of quadrilaterals start or end) and irregular nodes (where n ≠ 4 quadrilaterals meet) reduces the requirements on quad-meshing and increases the flexibility for polyhedral design with associated smooth surfaces. This paper introduces a family of piecewise polynomial, geometrically continuous surface constructions that yield good highlight line distributions also in the presence of irregular nodes next to a T-gon. Such tight juxtaposition can further reduce the quad-meshing requirements and increase the space of polyhedral design control structures. The surfaces can be chosen to cover T-gons with G ¹ caps of degree bi-4 - or with caps of degree bi-3 that are almost G ¹ and preserve the good highlight line distribution of the bi-4 G ¹ surfaces.