Characterization of analysis-suitable T-splines

• We study the analysis suitable T-spline spaces as a piecewise polynomials space.
• We characterize the difference between two neighboring polynomial expressions.
• We study when the space can be described by smoothness conditions.

In this article we provide the characterization of analysis suitable T-spline spaces (Beirão da Veiga et al., 2013) as the space of piecewise polynomials with appropriate linear constrains on the subdomain interfaces. We describe AST-meshes for which the linear constrains are equivalent to smoothness conditions and provide examples showing that this is not always the case.