Planar point set fairing and fitting by arc splines

Abstract We fair and fit planar point sets by minimal-energy arc splines. The fairing process consists of two steps: computing the optimal tangents for curve interpolation and adjusting the point positions by smoothing the discrete curvatures. To fit the point set with minimal-energy arc curve, a simple linear algorithm is given for computing the optimal tangents. The discrete curvatures derived from the optimal tangents can be made smooth by low-pass filtering. These two linear and local algorithms are combined to generate a fair point set together with a fair G1 arc curve within a given tolerance of the original data. The method can be used for fair shape design and measured data processing. Numerical examples are given to show the efficiency of this method.

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