变次数B-样条曲线

Multi-degree B-spline curves

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 （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 C^-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 effeetively spline curves＇ control points and knot vectors while keeping the desired accuracy, geometric design and data transmission of CAD system. reduce the numbers of which are very good for