Enhanced 3D parameterization for integrated shape synthesis by fitting parameter values to point sets

Abstract

Enhanced single-patch NURBS (Non-uniform rational B-splines) parameterization is developed based on fitting parameter values, capable of handling dynamically changing shapes. With respect to NURBS and T-splines, the proposed single-patch parameterizations results in lower dimensionality enabling optimizers to operate on geometric parameters. Avoiding subdivision surfaces and continuity problems for piecewise NURBS and reparameterizations for T-splines accelerates optimization. This parameterization may be an approximation or initial solution for piecewise NURBS and T-splines. These numerical benefits are accomplished using a multi-stage methodology. An augmented set of fitting variables is formulated beyond the weight factors and control points with parameter values of data points. This augmented set is structured to possess reasonable dimensionality. The developed non-linear fitting includes gradient-based minimization with respect to the augmented set and evolutionary error minimization using external functions. The benefits and potential difficulties of the procedure are evaluated thoroughly. The methodology is tested on engineering objects of high shape complexity and demonstrated to provide superior single- patch fitting performance compared to standard linear fitting methods. The developed numerical approach provides for the aspired main objective which is sufficiently accurate and numerically efficient dynamic shape parameterizaton using a compact set of shape parameters.