Curve and surface fitting models based on the diagonalizable differential systems

Curve and surface fitting is an important problem in computer aided geometric design, including many methods, such as the B-spline method, the NURBS method and so on. However, many curves and surfaces in the natural or engineering fields need to be described by differential equations. In this paper, we propose a new curve and surface fitting method based on the homogeneous linear differential systems. In order to approximate general curves or surfaces well, the diagonalizable differential systems with variable coefficients are adopted, which have explicit solutions. The fitting algorithms are presented for curves and surfaces from discrete points. Some numerical examples show that the two algorithms can obtain good fitting accuracy as the B-spline method.