Abstract
A mesh is locally quad-dominant (lqd) if all non-4-sided facets are surrounded by quadrilaterals. Lqd meshes allow for irregular nodes where n ≠ 4 quads meet and for multi-sided facets, called T-gons, that end quad-strips and so adjust mesh density. This paper introduces a new class of bi-cubic (bi-3) Geometric T-joint (GT) splines whose control nets are τ-nets, i.e. T-gons surrounded by quads. These GT-splines join smoothly with each other, bi-3 G-splines and regular C (1) bi-quadratic splines to form smooth surfaces of degree at most bi-3.