High precision B-spline curve fitting algorithm of measure points

To improve curve reconfiguration efficiency, the key points selection algorithm was proposed and applied in B-spline curve approximation of 3D measure points. The measure points with curvature extrema were selected as initial key points according to the analysis of discrete curvature. The knot vector established by the key points and the parameter values of the measure points which guaranteed a full-rank interpolation matrix. The unknown control points of the B-spline curve were determined by the least squared method. Hausdorff distance was used to measure the deviation between the given points set and the approximated curve. New key points were selected by the deviation and multi-point adjusting algorithm according to the analysis of shape index. Final key points and control points meeting the specified tolerance requirement were acquired through iterations. Experimental results demonstrated that the new algorithm was superior comparing to other methods in the aspects of the number of the control points, the number of iterations and the computation time.