Curves reconstruction from ordered point cloud data

In this paper an efficient curve reconstruction algorithm is presented. The algorithm divides the given ordered point set into subsets, the points in each subset are fitted by a quadratic curve based on Least-Square principle and all the given ordered points are fitted by a piecewise quadratic curve consisting of fewer curve segments. The freedom degrees of the reconstructed curve are divided into two groups: one group is to guarantee high fitting precision and the other group is to guarantee the smoothness of the curve. The reconstructed piecewise curve reaches high approximation accuracy and C¹ continuity. The method is simple and reliable and it is very useful in reverse engineering.