Evolutionary Optimization of Approximating Triangulations for Surface Reconstruction from Unstructured 3D Data

This article presents a study of the application of Computational Intelligence (CI) methods to the problem of optimal surface reconstruction using triangulations and NURBS (Non-Uniform Rational BSplines) surface approximations on digitized point data. In mechanical engineering surface reconstructions are used to transform physical objects into mathematical representations for computer aided design purposes. In order to record the geometrical shape of the objects, tactile or optical sensors generate point sets with a huge number of sample points. The number and distribution of these points are decisive for the quality and computational efficiency of the numerical surface representations. Triangulations and NURBS are widely used in CAD/CAM-applications, because they belong to a class of very flexible discrete interpolation and approximation methods. In order to verify the suitability of surface model independent point selection schemes and to find model dependent sampling point distributions, optimal surface reconstructions are used.