基于离散曲率的三次均匀B样条的局部光顺算法

摘要

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 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 this algorithm the curves are faired through adjusting the second discrete curvature of the corresponding control points directly, thus the fairing process is more concise and has stronger geometrical intuition. The experiment examples show that the algorithm can get better faring effects.