均匀B样条1次升降多阶的矩阵表示

The Matrix Representation for Multi-Degree Reduction or Elevation of Uniform B-Spline Curves

研究了均匀B样条曲线的1次升降多阶的矩阵表示,提出了将计算过程表示为多个矩阵连续相乘的形式,矩阵的乘积作为B样条升降阶的转换矩阵,得到B样条曲线升降阶后的控制顶点矢量可以表示为转换矩阵与原曲线控制顶点矢量乘积的形式.该方法不需要使用节点插入、节点删除和节点优化技术,具有模块化、可扩展性、便于实现等优点.

Multi-degree elevation and degree reduction of B-Spline curves in a matrix representation was proposed The control points of the degree elevated or reduced B-Spline curve can be obtained as a product of the transfor- mation matrix and the vector of original control points. The method does not need knots inserting or knots refin- ment. In this way, the process of degree changing of B-spline simply express.