Adaptive data fitting by the progressive-iterative approximation

In this paper, we develop the adaptive data fitting algorithms by virtue of the local property of the Progressive-iterative approximation (abbr. PIA), which generates the fitting curve (patch) by adjusting the control points of a blending curve (patch) iteratively. In the adaptive data fitting algorithms, the control points are classified into two classes, namely, active and fixed control points, and only the active control points need to be adjusted in each iteration, thus saving computation greatly. Lots of examples and experimental data are presented to demonstrate the efficiency of the adaptive data fitting algorithm. Since the PIA method can be made parallel easily, the adaptive data fitting algorithm developed in this paper has important applications in parallel large scale data fitting.

► Some bounds are proved, which state when it is safe to fix a point while guaranteeing a prescribed fitting precision.
► An adaptive data fitting algorithm is developed, which adjusts only the active control points.
► Some examples are presented to illustrate the efficiency of the adaptive data fitting algorithm.