Wavelet Analysis And Reconstruction Of NURBS Curvers And Surfaces

The modeling technology of non-uniform rational B-spline (NURBS) curves and surfaces and the wavelet technology are new technologies developed in the 1980's. The wavelet method has many advantages which the other methods can not be compared with. Using wavelet method to model B-spline curves and surfaces, we have got many good results. So the research of modeling technology of curves and surfaces based on wavelet method is very important.The dissertation researches mainly the algorithms of wavelet decomposition and reconstruction of pre-uniform and uniform B-spline curves and surfaces and new algorithm of decomposition and reconstruction of NURBS curves. The content is as follows:The algorithm of wavelet decomposition and reconstruction of pre-uniform B-spline curves and surfaces is studied. The idea of wavelet analysis of pre-uniform B-spline curves and surfaces is given, and the algorithm of wavelet composition and reconstruction of pre-uniform B-spline curves and surfaces is tried to extend to B-spline curves and surfaces. The complementary research is made on this algorithm.Based on the algorithm of wavelet composition and reconstruction re-uniform B-spline curves and surfaces, research on the algorithm of wavelet decomposition and reconstruction of uniform B-spline is made. Actually,the difference between the wavelet analysis and reconstruction of uniform B-spline and re-uniform B-spline curves and surfaces is that the wavelet after decomposition of the uniform B-spline curves and surfaces can be expressed consistently in the domain and on the boundary.The modeling technology of the multi-resolution editing of NUBS curves and surfaces is given and the existing results are researched further and improved. The new algorithm of wavelet composition and reconstruction of semi-orthogonal B-spline is researched. At the same time, the algorithm of wavelet composition and reconstruction of NURBS curves with integral order and non-integral order resolutions is obtained. And the wavelet composition of arbitrary order NURBS curves is realized. For a NURBS curve, semi-orthogonal decomposition and reconstruction can be done whether there are how many control points without the limits of the amount of control points. In this sense, the algorithm realized the modeling of curves of continuous resolution and the accurate composition and reconstruction is made for NURBS curves.In this sense, the algorithm realized the modeling of curves of continuous resolution and the wavelet composition and reconstruction of NURBS accurately without the limits of the number of control points.