How to calculate cubic bezier curve control points

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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.

Posted 27-Apr-11 8:25am

Member 2784779

Updated 27-Apr-11 10:25am

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Manfred Rudolf Bihy 27-Apr-11 16:11pm

Unclear to say the least.
If you only have the origin and the destination point the best you can hope for is a straight line. Please formulate your exact requirments in four or more statements.
Thanks for your cooperation!

Manfred Rudolf Bihy 27-Apr-11 16:39pm

Thanks for improving your question! See my answer for a link to a CP article that should help you!

Member 2784779 28-Apr-11 4:13am

Manfred, thank you for fast answer. This is what I need!

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Manfred Rudolf Bihy · Accepted Answer · 2011-04-27T10:40:00

Solution 1

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

Posted 27-Apr-11 10:40am

Manfred Rudolf Bihy

Comments

Sergey Alexandrovich Kryukov 27-Apr-11 22:16pm

Could help, my 5.
--SA