三次贝塞尔曲线上的最近点? [英] Closest point on a cubic Bezier curve?

问题描述

如何沿三次贝塞尔曲线找到最接近平面中任意点 P 的点 B(t)?

解决方案

经过大量搜索，我找到了一篇论文，其中讨论了一种在贝塞尔曲线上找到与给定点最近的点的方法:

<块引用>

改进代数算法点贝塞尔曲线的投影，由陈晓貂、尹舟、舒振宇、华苏和让-克洛德·保罗.

此外，我发现了维基百科和MathWorld 对 Sturm 序列的描述对理解算法的第一部分很有用，因为论文本身的描述不是很清楚.>

How can I find the point B(t) along a cubic Bezier curve that is closest to an arbitrary point P in the plane?

解决方案

After lots of searching I found a paper that discusses a method for finding the closest point on a Bezier curve to a given point:

Improved Algebraic Algorithm On Point Projection For Bezier Curves, by Xiao-Diao Chen, Yin Zhou, Zhenyu Shu, Hua Su, and Jean-Claude Paul.

Furthermore, I found Wikipedia and MathWorld's descriptions of Sturm sequences useful in understanding the first part of the algoritm, as the paper itself isn't very clear in its own description.

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