Affiliations: [a] Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India | [b] Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Abstract: 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 fit-ting from point clouds needs estimation of order, i.e. number of knots and a good parameterization model, i.e. the determination of parameter values of the digitized points in order to perform least squares (LSQ) fitting. Numerous work have been done on selection of such parameters. Nevertheless, the problem of LSQ with optimal knots has not been addressed in totality. Simultaneous optimization of number of knots and parameter values leads to multiple contradictory objectives and traditional optimization is prone to fail. The present work proposes a hybrid approach based on genetic algorithms, for optimal number of knots and optimal parameter allocation, simultaneously, for curve and surface fitting. A novel population initial-ization scheme involving analytical and neural network estimation is also proposed here, ensuring that the optimization procedure is both global in nature and computationally less expensive. Further classical opti-mization of parameters alone based on error is carried if required. The present study of parameterization is for Non Uniform B-spline fitting.
