Analysis-Suitable T-splines are Dual-Compatible

In this paper we define Dual-Compatible (DC) T-splines, and we prove that Analysis-Suitable (AS) T-splines are Dual-Compatible. We show that the classical construction of a dual basis for tensor-product T-splines easily generalizes to DC T-spline spaces, and we discuss in the last section of the paper how it paves the way to a mathematical theory of AS T-splines.

► We define Dual-Compatible (DC) T-splines.
► We prove that Analysis-Suitable (AS) T-splines are Dual-Compatible (DC).
► We construct a dual basis for Dual-Compatible (DC) T-spline spaces.
► We discuss how it paves the way to a mathematical theory of AS T-splines.