基于离散曲率的三次均匀B样条的局部光顺算法

在研究B样条曲线节点的曲率和对应控制点的离散曲率之间关系的基础上,引入了一种新的离散曲率——第二离散曲率的概念,得出了三次均匀B样条曲线节点的曲率和对应控制点的第二离散曲率成正比的结论,并给出了基于第二离散曲率三次均匀B样条曲线的光顺算法.该算法通过直接调整控制点的第二离散曲率进行曲线的光顺,从而使光顺过程更为简洁、更具几何直观性.算例表明,该算法具有较好的光顺效果.

On local fairing algorithm for cubic B-spline with discrete curvature

On the basis of investigating the relationship between the curvature of B-spline curves and the discrete curvature of its corresponding control points,a new conception of discrete curvature,the second discrete curvature is introduced.It is obtained that the curvature of cubic uniform B-spline curve at its joining points is proportional to the second discrete curvature of the corresponding control points.The fairing algorithm for cubic uniform B-spline based on the second discrete curvature is given.With thi...