Quasi-interpolation for analysis-suitable T-splines

We propose a novel local approximation method for analysis-suitable T-spline (AS T-spline) spaces via quasi-interpolation. The quasi-interpolants are defined as linear combination of the approximated function's values at appropriately chosen points. Benefited from the inherent nice properties of AS T-splines, the proposed quasi-interpolants can reproduce polynomials up to the same degree of AS T-spline spaces and can provide optimal approximation order. Some numerical examples of specific quasi-interpolants for bi-cubic AS T-splines are investigated to show the stability and efficiency.