Research On B-spline Curves And Surface

In this paper, the B-spline basis functions is given with two parameters of quadraticB-spline basis functions, the introduction of two parameters adjustment increased theflexibility of curve. At the same time two parameters of the spline curve expression aregiven by the method of tensor product, The quadric B-spline with two parameters canexpress the same curve as cubic Bézier curve can. The paper has five chapter: In chapter1,firstly, we introduce simply the development of CAGD and the main contents of thispaper. In the second chapter, some definitions and properties of Bézier, B-spline curvesurface are reviewed. Chapter3is the main part of research in this paper, we first introducethe spline function with two parameters, and then the author give the B-spline curve of twoshape parameters, and give the related properties and proof. The definition of the surfacecurve and surface satisfy some properties of uniform B-spline curves and surface. In thefourth chapter, Bézier, uniform cyclic B-spline curve matrix calculation formula researchachievements are introduced. Then the author gives the matrix expression of B-splinecurve by the tensor product method. Using the method of matrix, we calculated and discussthe three, four order uniform B-spline while it isC1continuous, and the conditions whichthe control vertex should satisfy, this indicates the matrix in calculations is more convenient.Finally, in chapter5, the author summarizes the full text work, innovation points andtheoretical and practical significance, and future research direction in the future.