  The paper considers the extension of the T-spline approach to the Generalized
B-splines (GB-splines), a relevant class of non-polynomial splines. The
Generalized T-splines (GT-splines) are based both on the framework of classical
polynomial T-splines and on the Trigonometric GT-splines (TGT-splines), a
particular case of GT-splines. Our study of GT-splines introduces a class of
T-meshes (named VMCR T-meshes) for which both the corresponding GT-splines and
the corresponding polynomial T-splines are linearly independent. A practical
characterization can be given for a sub-class of VMCR T-meshes, which we refer
to as weakly dual-compatible T-meshes, which properly includes the class of
dual-compatible (equivalently, analysis-suitable) T-meshes for an arbitrary
(polynomial) order.
