Combined Surface Reconstruction And Fairing For Wrap-around Models Based On Massive Points

With the development of the current digital measuring technology, Reverse Engineering technology has been more and more widely applied in geometric modeling, image processing and digital manufacturing etc. Surface reconstruction and fairing based on massive data is the key technologies of reverse engineering, and they are also the keystone and nodus of reverse engineering. In this paper, taking a class of wrap-around free-form surfaces for example, based on B-spline surface technology, the parameterization of massive data from wrap-around model, surface modeling, smooth joining and fairing are systematically studied.(1) With consideration of the measured massive data, a method of recognizing the projection axis from sampled points is given. Then, region segmentation and parameterization of points are realized by means of 3D/2D mapping and Coons surface construction. B-spline surface patches are finally reconstructed from segmented point sets. This algorithm avoids the disadvantage of human-computer interaction, so it is very helpful to improve the efficiency and automation of modeling process.(2) Taking the wrap-around surface model for example, for the smooth connection of two bi-cubic B-spline surfaces, a smooth connection method with G~1 geometric continuity is provided between two adjacent patches. Based on the algorithm of smooth connection of two bi-cubic B-spline patches, a smooth connection method of four bi-cubic B-spline patches which have the same corner is given.(3) With consideration of the smooth connected surfaces obtained previously, using the principal of discrete energy method, an algorithm which by adjusting the control points to reduce the grid energy so as to smooth the surface is provided. This algorithm can well maintain the original shape of the surface. It is speed, and also easy to programming realization. At last, use the method of reflection lines of Imageware to evaluate the quality of the blending surface.(4) Three practical examples are used to verify the validity of proposed algorithms. The first practical example is modeling and smooth connection of two wrap-around models, the second practical example is smooth connection of four patches with the same corner. These two examples show that the proposed algorithm is speed in surface modeling and high precision in smooth connection. The third practical example is fairing the surfaces after smooth connection. The analysis results indicate that the proposed fairing approach can fair the surfaces quickly and effectively.