基于局部能量的三次 B 样条曲线自动光顺算法

摘要

给出B样条曲线的一种自动光顺算法，通过求解一个以修改控制顶点为目标函数的优化问题，进而求出光顺后的控制顶点，反复上面的过程，直到最后得到满足约束条件的光顺后的曲线。通过光顺法光顺后的曲线，不仅使曲线的曲率变化比较均匀，而且也使曲线的应变能较小，光顺效果明显。%Local Energy Fairing of parametric cubic B‐spline curves is presented in this paper .Firstly ,we summarize all kinds of fairing criteria for curves fairing and select most suitable fairing criteria for the pro‐posed algorithm .Secondly ,by solving an optimization problem of having constraint condition ,we obtain the fairing control points .Lastly ,fairing curve is got by repeating process above .Fairing curves are acquired . Through this paper ,the curve of the ray becomes smooth .Not only the curvature of the curve is more uni‐form ,but also the strain of the curve can be smaller ,so the effect is obvious .