A shape controled fitting method for Bézier curves

The problem of controling a shape when fitting a curve to a set of digitized data points by proceeding to a least squares approximation is considered. A nonlinear method of solving this problem, dedicated to the obtention of planar curves with a smooth and monotonous variation of curvature is introduced. This method uses particular Bezier curves, called typical curves, whose control polygon is partially constrained in order to provide the desired curve shape. The curve fitting principle is based on variations of the tangent direction at the ends of the curve. These variations are controled by the displacement of a given curve point. An automatic procedure using this method to get a curve close to a set of data points has been implemented. An application to car body shape design and a comparison with the least squares approximation method is presented and discussed.

[1]  Horst Nowacki,et al.  Fairing Bézier curves with constraints , 1990, Comput. Aided Geom. Des..

[2]  Mamoru Hosaka,et al.  Generation of High-Quality Curve and Surface with Smoothly Varying Curvature , 1988, Eurographics.

[3]  Gerald E. Farin,et al.  Fairing cubic B-spline curves , 1987, Comput. Aided Geom. Des..

[4]  Gerald E. Farin,et al.  Curvature and the fairness of curves and surfaces , 1989, IEEE Computer Graphics and Applications.

[5]  Thomas Reuding,et al.  Smoothing rational B-spline curves using the weights in an optimization procedure , 1995, Comput. Aided Geom. Des..