如何计算三次贝塞尔曲线控制点 [英] How to calculate cubic bezier curve control points

问题描述

我有一条曲线，该曲线由与线连接的点的集合显示.我必须用一条三次贝塞尔曲线代替这种曲线.我有起点和终点，但是我不知道如何计算两个控制点.

问题已改善:

我的曲线包含4个点(p0，p1，p2和p3). p0是起点，p3是终点. p1和p2是中间的两个点.如果我连接这4个点，我将得到3条线.我想用三次贝塞尔曲线代替那条三线曲线.为此，我必须计算三次贝塞尔曲线的两个控制点的位置.我的问题是如何?
同时，我发现的文章很少( http://www.moshplant.com/direct-or/bezier/math .html [^ ] )，它描述了如何绘制三次贝塞尔曲线，因此我将尝试对这些公式进行逆向工程以获得控制点.

I have curve that is displayed by collection of points connected with lines. I have to replace that kind of curve with one cubic bezier curve. I have origin and destination point, but I don''t know how to calculate two control points.

Question improved:

I have curve consisting of 4 points (p0, p1, p2 and p3). p0 is origin point and p3 is destination point. p1 and p2 are two point in the middle. If I connect these 4 points I will get 3 lines. I want to replace that 3-line-curve with cubic bezire curve. To get that, I have to calculate positions of two control points of cubic bezier curve. My question is how?
In meantime I found few articles (http://www.moshplant.com/direct-or/bezier/math.html[^]) that describes how to draw cubic bezier curve, so I will try to reverse-engineer these formulas to get control points.

推荐答案

请在此处查看:通过带有Bezier基本体的一组2D点绘制平滑曲线 [

Please have a look here: Draw a Smooth Curve through a Set of 2D Points with Bezier Primitives[^]. The article is for C# but since you didn''t specify any language I thought I just post this.

Best regards,

-MRB

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