Spline Toolbox

Knot Multiplicity

The multiplicity of the knots governs the smoothness, in the following way: If the number occurs exactly times in the sequence , then and its first derivatives are continuous across the break , while the th derivative has a jump at . You can experiment with all these properties of the B-spline in a very visual and interactive way using the command bspligui.

B-form

B-Spline Properties