Constrained least square progressive and iterative approximation (CLSPIA) for B-spline curve and surface fitting

Combining the Lagrange multiplier method, the Uzawa algorithm, and the least square progressive and iterative approximation (LSPIA), we proposed the constrained least square progressive and iterative approximation (CLSPIA) to solve the problem of B-spline curve and surface fitting with constraint on data interpolation, i.e., computing the control points of a B-spline curve or surface which interpolates one set of input points while approximating the other set of given points. Compared with the method of solving the linear system directly, CLSPIA has some advantages as it inherits all the nice properties of LSPIA. Because of the data reuse property of LSPIA, CLSPIA reduces a great amount of computation. Using the local property of LSPIA, we can get shape preserving fitting curves by CLSPIA. CLSPIA is efficient for fitting large-scale data sets due to the fact that its computational complexity is linear to the scale of the input data. The many numerical examples in this paper show the efficiency and effectiveness of CLSPIA.