B-spline Curve Reconstruction from Local Fitting to Whole Fitting in Computer Aided Geometric Design

In B-spline curve reconstruction to a set of ordered points, the numerical stability of the approximation system and the quality of reconstruction curve are unknown, these factors lead to the wiggle and deviation of the approximation curve. To avoid these problems, we propose a reconstruction algorithm from local fitting to whole fitting in this paper. This approach takes two steps: 1.Construct a curve with low degree by local fitting data points, which is named controlling curve. 2. Find another B-spline curve to approximate the controlling curve using the best least approximation. In this algorithm, the controlling curve has a arc-length parameterization , which reflects the distribution of the data points; and the system of this method is always positive so that we needn’t consider the singularity of this system.