B-Spline Method And Its Application In CAGD

Because of the advantages of B-spline, such as the strong ability of shape control, it is widely used in Computer Aided Geometric Design (CAGD), and non-uniform Rational B-spline (NURBS) was even made to be the only mathematical method of describing the geometry of industrial product. This paper focuses on the non-uniform B-spline curve, corresponding simple algorithm were designed for several common geometric operations. The B-spline surface geometry modeling was conducted from positive and reverse perspective, respectively. The following are main tasks of the paper:(1)According to the characteristics of B-spline basis function’s definition formula, a fast algorithm was designed, laying a foundation for subsequent operation about the B-spline.(2)After analyzing the recursive characteristics of B-spline basis function, the feature was applied to equidistant sampling of B-spline curves, the experiment results show that the effect is superior to the equal parameters sampling method.(3)Through the study of the formal derivation of B-spline curves, the guide curve, each point of the tangent vector and the curvature distribution were gained, the method has avoided the complex direct derivation operation. The node insertion algorithm to B-spline curve was also completed, and the flexibility was increased control shape in the interaction design.(4)In addition to construct B-spline curve and surface according to the known parameters, for a given measurement data points, the research has highlighted the B-spline curve and surface reconstruction technology,3D surface models were finally obtained, and the application of B-spline method in CAGD was verified.