Abstract: The use of progressive iterative approximation (PIA) to fit data points has received a deal of
attention benefitting from its simplicity and flexibility. To obtain a fitting curve satisfying the shape
high fidelity, we present an adaptive B-spline curve fitting algorithm based on regularized progressive
iterative approximation (RPIA) and the selection of dominant points. Firstly, the initial dominant points
are selected from the given points in terms of curvature estimates and an initial progressive iterative
approximation curve is constructed. Then the fitting curve based on RPIA is updated by means of the
fitting error and the selection of refinement dominant points according to the curvature distribution of
given points. The fitting curve possesses fewer control points at flat regions but more at complex
regions. By the use of a regular parameter, progressive iterative approximation is generalized and the
flexibility of PIA is promoted. Finally, numerical examples are provided to demonstrate that compared
with the conventional least square approaches the proposed method can achieve a higher fitting
precision with far fewer control points.

Key words: B-spline curve fitting, regularized progressive iterative approximation, adaptive refinement;
curvature estimation