A compact algebraic representation of cardinal GB-splines

This work introduces a compact algebraic representation of generalized B-spline basis functions built upon uniform knot partitions (also known as cardinal GB-splines), that stands out for its simplicity with respect to the well-known integral formulation. Moreover, this result clarifies the relationship between cardinal GB-splines and classical polynomial B-splines, as it isolates the polynomial component of a GB-spline from the non-polynomial contribution brought by the two non-monomial generators of the function space.