变次数B-样条曲线

变次数B-样条（MD-样条）曲线是在不同区间有不同次数的特殊B-样条曲线.为了适应CAD造型系统的发展，研究了最大变化次数小于3的MD-样条曲线.这类MD-样条继承了多项式B-样条的变差缩减性、保凸性等大多数性质,并具有退化性、嵌入节点等独特性质.整个MD-样条曲线至少是Cn-1连续的,这里n为整个曲线段的最小次数.研究了MD-样条与B-样条的关系,可以通过嵌入节点将MD-样条转化为B-样条,同时通过MD-样条能够将B-样条的升阶看成是几何割角的过程.变次数B-样条能够在保持理想精度的条件下,有效地减少控制顶点和节点向量的数目,有利于几何设计和CAD系统的数据传输.

Multi-degree B-spline curves

Multi-degree B-spline (MD-spline) curves are special B-spline curves with various degrees on different intervals, thus adapted to the development of CAD modeling system. MD-spline curves whose maximal variational degree was lower than three were investigated. This kind of MD-splines inherit most properties of polynomial B-splines, such as variation diminishing property, convexity preserving property, etc, and enjoy other advantageous properties for modeling, such as degeneration property, knot insertion property. Also the whole MD-spline curve is at least Cn-1, where n is the smallest degree of whole curve segments. In addition, the relation between MD-spline and B-spline was presented. MD-spline can be transformed into B-spline through knot insertion, simultaneously the degree elevation of B-spline can be interpreted as corner cutting process through MD-spline. MD-splines can effectively reduce the numbers  of spline curves control points and knot vectors while keeping the desired accuracy, which are very good for geometric design and data transmission of CAD system．