本项目研究变次数B样条的升阶性质及应用。变次数B样条打破B样条非零段次数相同的限制，允许次数不同。因此，在高低次段拼接时，低次多项式不需要用高次多项式表示，从而能减少数据量和计算量。B样条的升阶，每段次数都升高，具有整体性。相比之下，变次数B样条的升阶，可以仅升某段的次数，而其余段次数保持不变，具有局部性，升阶情况灵活多样。并且，B样条的升阶能通过变次数B样条的升阶表示成控制顶点几何割角的过程。由此可见，变次数B样条的升阶，优点突出。但是，由于次数变化的复杂性，现有的升阶理论，仅适用于双次数的情况。本项目旨在克服困难，发掘新思路，探索新方法，建立变次数B样条在次数任意可变情况下的一般升阶理论，以满足CAD造型系统的要求。项目研究方案首先从基函数的升阶公式入手，接着给出曲线的升阶公式，进而设计变次数B样条曲线与B样条曲线相互转换的算法，以适应几何模型转换的需求，使其能在CAD中发挥巨大作用。

This project studies the degree elevation property and its applications of changeable degree B-splines in CAD. Changeable degree B-spline breaks the limit of the same degree property of nonzero piecewise polynomials in any B-spline and allows different degrees. Thus, when a low-degree segment is connected with a high-degree segment, low-degree polynomials do not need to be represented by high-degree polynomials, so the data size and computation load are both reduced. For B-spline, degree elevation is a global property, since the degrees of all the polynomial segments are raised together. Compared with it, the degree elevation property of changeable degree B-spline is local, because that for this kind of spline, when the degree of one segment is raised, the degrees of the other segments can be kept. Moreover, through degree raising of changeable degree B-spline, the degree elevation process of B-spline can be represented as a geometric corner-cutting form of control points. This shows that the degree elevation property of changeable degree B-spline has many advantages. However, for the complexity of degrees, the theory of degree elevation of changeable degree B-spline only applies to the two-degree cases. This project aims to overcome difficulties, explore new ideas and methods, and establish a generalized theory of the degree elevation of changeable degree B-spline. This theory is needed to be appropriate for the cases of arbitrary degrees and meet the needs of CAD modeling systems well. Firstly, the degree elevation formulas of basis functions of changeable degree B-spline will be studied. Next, the degree elevation formulas of changeable degree B-spline curves. And then, the conversion algorithms between B-spline and changeable degree B-spline are designed, which meet the conversion requirements of geometric models, and play a huge role in CAD.