Reconstructing B-spline Curves from Point Clouds – A Tangential Flow Approach Using Least Squares Minimization

We present a novel algorithm based on least-squares minimization to approximate point cloud data in 2D plane with a smooth B-spline curve. The point cloud data may represent an open curve with self intersection and sharp corner. Unlike other existing methods, such as the moving least-squares method and the principle curve method, our algorithm does not need a thinning process. The idea of our algorithm is intuitive and simple — we make a B-spline curve grow along the tangential directions at its two endpoints following local geometry of point clouds. Our algorithm generates appropriate control points of the fitting Bspline curve in the least squares sense. Although presented for the 2D case, our method can be extended in a straightforward manner to fitting data points by a B-spline curve in higher dimensions.