Abstract: To use B-spline curve and surface to fit data with an underlying function having
discontinuous points and/or cusps, the fitting results obtained by least squares method are often bad in
the vicinity of discontinuous points and cusps because of the fixed B-spline knots. In this paper, we
propose a method for solving data fitting problem with cubic B-spline curve and surface by using
differential evolution algorithm. Our method can set B-spline knots adaptively, so as to optimize the
number and location of knots simultaneously and produce quasi-multiple knot in the vicinity of
discontinuous points and cusps. With this, we can fit data with an underlying function having
discontinuous points and/or cusps with high precision.

Key words: data fitting, B-spline curve and surface, least squares method, differential evolution
algorithm, adaptation, quasi-multiple knot