Fitting Data Using Piecewise G1 Cubic Bezier Curves

摘要

A method is described for least squares filling an ordered set of data in theplane with a free-form curve with no specific function or parameterization given for the data. The method is shown to be effective and uses some techniques from the field of Computer Aided Geometric Design (CAGD). We construct a piecewise G cubic Bezier curve from cubic curve segments which have as their initial end points, or knot points, some of the data points. The parameters for the curve are: the knot points, the angles of the tangent vectors at the knot points, and the distances from each knot point to the adjacent control points. The algorithm is developed and three solution curves are presented: Globally Optimized Only (GOO), Segmentally Optimized Only (SOO), and Segmentally then Globally Optimized (SGO). (AN).