# Geometrically Continuous Isogeometric Test Functions

Geometrically Continuous Isogeometric Test Functions

In many practical applications rectangular control meshes of arbitrary topological type are needed. Such meshes may contain vertices of valency ̸ = 4 (so called irregular vertices). Using the standard tensor product setup one can not obtain C 1 continuous spline surface over the whole mesh. However, one may try to construct at least geometrically continuous spline surface. In the talk we will borrow the Reif’s approach for constructing G 1 smooth surface based on biquadratic rectangular B´ezier patches and use it for the IgA. IgA is an approach that uses the NURBS representation of a CAD model to construct the space of test functions which are used for the simulation. Since the G 1 conditions at irregular parts are inevitable, not all control points are free to choose but are subject to some linear constraints which form a homogeneous linear system. Since for IgA setting the reﬁnement approach is very important, we will show how to reﬁne the surface and how the system of constraints reﬁnes. The main goal of the talk will be to construct a basis (geometrically continuous isogeometric test functions) of the kernel of this linear system after few steps of the reﬁnement.