Generalized B-Splines and Knot Insertion Algorithm

A new representation to splines is introduced and the concept of generalized Bsplines is presented by considering the null space of a second order constant coefficient differential operator and the(unique) solution to an initial-value problem;it shows the evaluation algorithm and knot insertion algorithm for generalized B-splines and analyses convex-hull property and variation-diminishing result.At last,some examples show that the algorithm is valid to all kinds of splines.