Study And Realization On Construction, Fairing And Smooth Joining Between Adjacent Of The NURBS Surface

Along with the rapid improvement of modern industry and Sci-Tech, modeling technology of curve and surface are becoming more and more maturity. Non Uniform Rational B-Spline (NURBS) is becoming the most outlooks modeling technology. It has been specified as a standard of industrial products geometry description method and has been widely used and recommended.The fairing and smoothing joining between adjacent of bicubic NURBS surfaces are studied. The main content includes the following four parts, (1) the construction of the NURBS surfaces, (2) the joining between adjacent of bicubic NURBS surfaces, (3) the fairing and smoothing of bicubic NURBS surfaces.In the first part, the chapter 3, Using surface interpolate directly, fairness of the surface could not be guaranteed. A new method of surface reconstruction which combine the interpolation with approximation is presented, and an algorithm composed of initial surface construction of partial interpolation, surface approximation of all given data and error analysis has been realized.In the part two, chapter 4, Joining between two bicubic NURBS surfaces which have the same boundary are studied, and a useful algorithm which satisfy G2 connectivity is introduced. Although it is based on bicubic NURBS surface, it can be easily improved to high degree which can be used widely. The algorithm is simplicity and rapidly for calculations. The realistic experiment data and the theory are referenced. An effective method of G2 connectivity of three bicubic NURBS surfaces which have the same corner is obtained. It also references the method of two NURBS surfaces joining and based on space projection of control points. It can be proved that all algorithms are feasible.The third part of paper, chapter 5, Focus on the boundary after the surfaces had been jointed. The curvature mapping and the line-frame map of the surfaces are produced. In terms of them the smoothing attributes of boundary is analyzed. It's explicitly, effective and subjective. As for the objective detection of smoothing, the shearing force degree is used to detect the bad point, which is known as the non-smoothing point, and a smoothing way based on it is introduced. The surface can be smoothed by means of changing the value of weight which near the bad point.The main conclusions of the dissertation are given in the last chapter, in addition to direction of next researches.