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.
A compact algebraic representation of cardinal GB-splines
Viscardi A.
2024
Abstract
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.
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