creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods.

A B-spline of order is a piecewise polynomial function of degree in a variable . It is defined over locations , called knots or breakpoints, which must be in non-descending order . The B-spline contributes only in the range between the first and last of these knots and is zero