Fitting freeform multi-parameter shapes to 3D data points - A case study

We present an approach of geometric fitting of freeform shapes to 3D data points, where the size of the fitting problem is relatively large. The shapes studied represent ship propeller blades of dimension up to 3m, with precision requirements of few trim. Moreover, the shapes are freeform, and designed using a geometric model dependent on hundreds of numerical parameters. For the ship industry it is crucial to optimally deal with the shape parameters in order to judge whether or not a particular manufactured part fits within the tolerances. We have developed a method to evaluate the shapes numerically and we report on the approach we took. The sensitivity of a deviation objective function with respect to critical design parameters could be acquired. Also some procedures for automated optimization were explored.