Piecewise Bézier Curve Fitting of a Point Cloud Boundary by Simulated Annealing

摘要

The determination of approximation curves and surfaces from a point clouds is an important task in CAD, in particular on reverse engineering. The determination of an approximation curve from a sequence of points is a known subject, however the surface approximation is still an open research field. This work presents a method to determine curves that approximates the boundaries of a point cloud. Initially, the set of points determining the boundary of the point cloud is presented. These sequences are approximated by piecewise cubic Bézier curve segments. A simulated annealing algorithm is used to determine the approximation curve by minimizing the discrepancy between the sequence of points and the piecewise curve. The curve length is used as regularization to avoid the overfitting problem. The results shows that the algorithm determined the curves that approximates the boundary of a point cloud.