Study On Modeling Method Of NURBS Complex Free Surface

In order to meet the needs of the rapid development of modern industrialization and reallife, curve and surface modeling techniques is increasingly seen as important. As the onlymathematical description of defining industrial products geometry, Non-Uniform RationalB-Spline(NURBS) shows the promise of powerful advantages in the field of aerospace,shipbuilding, automobile and mold.The modeling technology of complex free surface based on NURBS theory and theconstructed surface are analyzed and simulated in this dissertation. The main research contenthas been accomplished as followings:(1) Firstly, the modeling technology of cubic NURBS curves and surfaces are introducedin detail. Secondly, the matrix representation of cubic curves and bicubic surfaces based onthe definition and properties of NURBS curves and surfaces are given. Lastly, the matrixmethed is applied to construct an aircraft engine vane.(2) Proceeded from the recursive algorithm of B-spline, the matrixes representation forquartic B-spline base functions are derived by the use of the reasoning technology of symbol.On this basis, the representation of block matrixes for quartic NURBS curves and surfaces aregiven according to the rational fraction of NURBS surface.(3) The methods of determining node vector are given by parametric processing. Thetangent conditions and free end condition of quartic NURBS curve based on the definition ofparametric spline and the derivative of B-spline are deduced. The reverse calculationalgorithms of control points and weights are proposed. The quartic NURBS curves areconstructed with these parameters. On this basis, the quartic NURBS surfaces are constructedby skinning. Surfaces are generated in MATLAB lastly.(4) Bicubic and quartic NURBS surfaces are constructed with the same data points basedon modeling technology of complex free surface, and these surfaces are compared with thetheoretical surface. The error and fairness of these surfaces are analyzed in CATIA. Finally,the quartic NURBS surfaces are simulated to confirm its correctness and feasibility.