Parameter optimization for B-spline curve fitting using genetic algorithms

B-splines have today become the industry standard for CAD data representation. Freeform shape synthesis from point cloud data is an emerging technique. This predominantly involves B-spline curve/surface fitting to the point cloud data to obtain the CAD definitions. Accurate curve and surface fitting from point clouds needs a good parameterization model, i.e. the determination of parameter values of the digitized points in order to perform least squares (LSQ) fitting. Numerous works have been on the selection of such parameters. Nevertheless, it is difficult with the present approaches to estimate better parameters particularly when the points are irregularly spaced and lie on a complex base curve or surface. There is a need to evolve from all the available parameterization solutions an optimum set of parameters which in turn will generate curves/surface interpolating the given data closely. An approach based on genetic algorithms for parameter optimization is presented here. A novel population initialization scheme is proposed that ensures that the optimization procedure is both global in nature with less expensive convergence. The present study of parameterization is for non uniform B-spline curve fitting.