B样条曲线的降阶公式及近似降阶方法

Degree Reduction Formula and Approximate Degree Reduction of B-Spline Curves

已有的B样条曲线降阶方法 ,由于无降阶公式可循 ,对于可降阶曲线常要通过解一系列线性方程组来实现降阶 .该文给出了B样条曲线的降阶公式 ,使得可直接用降阶公式对可降阶曲线进行降阶 .利用降阶公式和约束优化方法 ,文中进一步给出了B样条曲线的一种近似降阶方法和相应的算法 ,使得在用约束优化方法求出可降阶的近似曲线后 ,就可直接用降阶公式求出降阶曲线 ,简化了降阶过程 .该方法应用范围广且简单实用 .

A degree reduction formula for B-spline curves is developed by means of the coefficient matrix of B-spline curves. It makes the degree reduction of the degree reducible B-spline curves easily realized by using the degree reduction formula directly instead of solving linear equation sets. Based on the degree reduction formula and the constrained optimization method, an approximate degree reduction method for general B-spline curves is presented and the algorithm for this method is proposed. The procedure of the degree reduction for B-spline curves is simplified with this method. We can get the degree reduction curves by using the degree reduction formula after obtaining the reducible approximate curves by the constrained optimization method. In addition, this method can be applied to all kinds of B-spline curves and the algorithm can be easily realized.