Constructing 2D curves from scanned data points using B-spline wavelets

Abstract

This paper describes a method for automatic reconstruction of concise polygonal curves from unorganized dense planar points. In reverse engineering, these planar points may be generated by slicing 3D data points and projecting them onto a plane. It is necessary to approximate these points by constructing 2D polygons, while keeping the shape error within a given tolerance. These 2D polygons can be used for fabrication using rapid prototyping processes. With the method outlined in this paper, the curve to fit these data points can be constructed without considering the structure, orientation and topology information of the points. The final 2D polygon obtained possesses the minimum number of points while keeping the shape error within a given tolerance. This is accomplished in several steps: firstly, the planar points are sorted by a tangent-vector based method, which uses a fixed neighbourhood size to estimate the tangent vector of a point. Secondly, the sorted points are decomposed into different levels by using B-spline wavelets. Finally, the polygonal curve is constructed from coarser to finer level under the control of shape error between the original planar points and constructed curve.