Nonnegative surface fitting with Powell-Sabin splines

Algorithms are presented for fitting a nonnegative Powell-Sabin spline to a set of scattered data. Existing necessary and sufficient nonnegativity conditions for a quadratic polynomial on a triangle are used to compose a set of necessary and sufficient nonnegativity constraints for the PS-spline. The PS-spline is expressed as a linear combination of locally supported basis functions, of which the Bernstein-Bézier representation is considered to improve the efficiency. Numerical examples illustrate the profit of nonnegative surface fitting with Powell-Sabin splines.