Abstract
The fitting of curves and surfaces has been widely used in computer-aided design and computer-aided manufacturing (CAD/CAM). However, traditional data fitting methods lack clear geometric meaning. By iteratively adjusting control points, the progressive-iterative approximation for least square fitting (LSPIA) algorithm can obtain the least square fitting results for given data points with intuitive geometric meaning, but the convergence rate is prolonged. Here, we design a novel LSPIA algorithm based on the conjugate-gradient method, named CG-LSPIA. First, the conjugate-gradient vector is constructed, and then the control points are precisely updated. The algorithm converges in at most $n$ iterations. We also demonstrate the convergence of CG-LSPIA. In the absence of numerical error, the numerical examples show that our method is effective and greatly reduces the iteration time for reaching the fitting error limit compared with the LSPIA.
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