B Spline Curve And Surface Reconstruction Based On Genetic Algorithm

Reverse engineering is a new subject and technology coming up with the development of computer science and data digitization. With reverse engineering technology, CAD geometrical models are reconstructed from existent objects, which can be processed by advanced technology. Curve and surface reconstruction which is an important part in reverse engineering is widely used in various fields such as aviation and automobile manufacturing industry, medical imaging, description topography and so on. This thesis mainly studies the reconstruction of B-spline cloesed curves and hierarchical B spline surfaces in reverse engineering. The main contributions are summarized as follows:1. Based on the analysis to the conventional approaches for B-spline curve fitting, it is pointed out that these approaches are easy to result in data redundancy. In curve fitting based on simple genetic algorithm, though node values and parameter values can be optimized at the same time, the number of control points of B-spline curve should be specified in advance. In order to overcome these deficiencies, a new approach of B-spline closed curve fitting to a set of ordered points is presented based on Messay genetic algorithm. In the process of evolutionary computation, a B-spline closed curve approximate to a set of ordered points within a given error is obtained by adaptively adjusting parameters sequence, node vector and the number of control points. And these adjustments are caused by constantly changing genes and gene number of chromosome in the population. With this approach, a B-spline closed curve satisfying the desired shape fidelity can be generated as long as a set of ordered points and the order of B-spline closed curve are inputed. This approach has strong adaptive capacity and can be applied ina intelligent curve modeling system. Some experimental results demonstrate its effectiveness.2. Some conventional approaches for hierarchical B-spline surface fitting are reviewed, and some shortcomings due to overall refining method and refined uniform rules are analyzed. In this paper, a local adaptive refinement approach for triangular mesh approximation with hierarchical B-spline surface is proposed. Firstly, the boundary of triangular mesh is fitted synchronously by genetic algorithm. Secondly, the first level B-spline surface interpolating boundary curve is obtained by least square fitting method. Thirdly, in the region exceeding a given error, genetic algorithm is used to optimize the surface adaptively while the B-spline surfaces at different levels keep C2 continuity. One level above another level, the local refinement fitting is carried out until meeting a given error. At last, the hierarchical B-spline surface fitting the triangular mesh within a given error is constructed. With this approach a less size of the control grid can be obtained. The B-spline surfaces generated by the approach can be used for multi-level network transmission and progressive show.