An Efficient Hybrid Optimization Strategy for Surface Reconstruction

Abstract

An efficient and general surface reconstruction strategy is presented in this study. The proposed approach can deal with both open and closed surfaces of genus greater than or equal to zero and it is able to approximate non-convex sets of target points (TPs). The surface reconstruction strategy is split into two main phases: (a) the mapping phase, which makes use of the shape preserving method (SPM) to get a proper parametrisation of each sub-domain composing the TPs set; (b) the fitting phase, where each patch is fitted by means of a suitable Non-Uniform Rational Basis Spline (NURBS) surface without introducing simplifying hypotheses and/or rules on the parameters tuning the shape of the parametric entity. Indeed, the proposed approach aims stating the surface fitting problem in the most general sense, by integrating the full set of design variables (both integer and continuous) defining the shape of the NURBS surface. To this purpose, a new formulation of the surface fitting problem is proposed: it is stated in the form of a special Constrained Non-Linear Programming Problem (CNLPP) defined over a domain having variable dimension, wherein both the number and the value of the design variables are simultaneously optimised. To deal with this class of CNLPPs, a hybrid optimisation tool has been employed. The optimisation procedure is split in two steps: firstly, an improved genetic algorithm (GA) optimises both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the solution provided by the GA constitutes the initial guess for the subsequent deterministic optimisation, which aims at improving the accuracy of the fitting surfaces. The effectiveness of the proposed methodology is proven through some meaningful benchmarks taken from the literature.