查找穿过N点的曲线的贝塞尔曲线控制点 [英] Find bezier control-points for curve passing through N points

问题描述

考虑以下很好的解决方案，以找到通过4个点的曲线的三次Bézier控制点:

Considering the following nice solution for finding cubic Bézier control points for a curve passing through 4 points:

我想知道，对于N> 2且N≤20而言，是否可以通过直接扩展使Bézier曲线通过N个点?

I wonder, if there is a straightforward extension to this for making the Bézier curve pass through N points, for N > 2 and maybe N ≤ 20?

推荐答案

这是一个非常老的问题，但是我留给将来有相同问题的人使用.

This is a really old question, but I'm leaving this here for people who have the same question in the future.

@divanov提到对于N> 4，没有Bezier曲线穿过N个任意点.

@divanov has mentioned that there's no Bezier curve passing through N arbitrary points for N >4.

我认为OP正在询问如何计算控制点以连接多个贝塞尔曲线以生成看起来平滑的单个曲线.

I think the OP was asking how to compute the control points to join multiple bezier curves to produce a single curve that looks smooth.

此pdf文件将向您展示如何计算控制点: http://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf

This pdf will show you how to compute the control points: http://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf

http://corner.squareup.com/Square的2012/07/smoother-signatures.html 讲述了它们如何绘制一条平滑曲线，该曲线穿过鼠标绘制的签名的所有采样点.

which I found on this writeup http://corner.squareup.com/2012/07/smoother-signatures.html from Square about how they render a smooth curve that passes through all the sampled points of a mouse drawn signature.

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