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This paper addresses the linear independence of T-splines that correspond torefinements of three-dimensional tensor-product meshes. We give an abstractdefinition of analysis-suitability, and prove that it is equivalent todual-compatibility, wich guarantees linear independence of the T-splineblending functions. In addition, we present a local refinement algorithm thatgenerates analysis-suitable meshes and has linear computational complexity interms of the number of marked and generated mesh elements.

Globally structured 3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement