We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, that is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays and boundedness of their cardinalities, nestedness of the generated T-spline spaces, and linear computational complexity of the refinement procedure in terms of the number of marked and generated mesh elements. 
Analysis-suitable adaptive T-mesh refinement with linear complexity