Curve Fitting with Bézier Cubics

1. An image’s outline cannot be fitted by a single cubic Bézier curve piece if it contains corners. Corners are points In this paper, a new curve-fitting algorithm is presented. This algorithm can automatically fit a set of data points with at which the outline’s directions take a sharp turn, or the piecewise geometrically continuous (G) cubic Bézier curves. outlines have discontinuous tangent values. The algorithm consists of two steps. During the first step, sig2. An image’s outline cannot be fitted by a single cubic nificant points are identified from the given data set and are Bézier curve if it contains more than two inflection points. further classified as either corners or joints. Curve fitting is 3. An image’s outline is difficult to be fitted by a single done in the second step. A weighted least-squares technique is used to find an optimal solution for the construction of piecewise piece of cubic Bézier curve if it has large curvature changes Bézier curves. The resulting Bézier curve segments will be along certain portion of the curve. smoothly connected at all joint points. This algorithm has Therefore, in most cases, an image’s outline will be fitted been applied to many digital images with good results.  1996 by using a piecewise approximation approach. A piecewise Academic Press, Inc. approximation to a shape consists of a number of cubic curves pieces connected end-to-end. The location and smoothness of the joints or knots between the pieces is