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This is a basic (and probably a stupid) question, math is not my forte and I don't know much about math, in this site:

http://www.ams.org/samplings/feature-column/fcarc-bezier

in the bezier curves column, specifically in the cubic bezier curve there are 4 points in a line namely p0 p1 p2 and p3.

In my case, I need to find the 2 control point in a line with a specific start and end point.

I can't understand where did the p1 and p2 came from.

and also, where could I get the tangent?

Please know that I am not a mathematician, I have a basic math knowledge and I'm poor at algebra and other kind of math, so please understand and explain as simple as you could do, I would appreciate it so much.

I have searched and found some links here as well, but I feel like I need a simpler answer than those (stupid right?) T.T

Please somebody help. And thanks in advance!

(I am trying to understand bezier curve better so I could make a function of that in objective c with specific number of points. And I'm assuming that the formula in that site will be helpful for my function as well.)

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  • $\begingroup$ What exactly are you wondering about? Do you have some function that you are trying to approximate with a curve? Or are you just trying to understand bezier curves better? Are you looking for the formula for Bezier curves? $\endgroup$ – Alan Wolfe Aug 3 '15 at 5:20
  • $\begingroup$ Oh sorry for not specifying, I am actually trying to make a function for making a cubic bezier curves with specific number of points via object c, but I can't understand bezier curves so I am trying to understand it better so I could make a function for that using uibezierpath in objective c $\endgroup$ – jane Aug 3 '15 at 5:23
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Bezier curves pass through the first and last control point, but in general do not pass through the others.

Your best bet for understanding Bezier curves to use them in a program is to start out by playing with them and seeing how they work and how moving control points affects the curve.

Here's a good place to start with that: http://demofox.org/bezcubic.html

You might also give this a read, that talks about some of the basics of bezier curves: http://blog.demofox.org/2014/03/04/bezier-curves/

Lastly, understanding the de casteljeau algorithm can help cement the intuition behind how bezier curves work: http://blog.demofox.org/2015/07/05/the-de-casteljeau-algorithm-for-evaluating-bezier-curves/

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  • $\begingroup$ Okay, I looked and I saw these formula again: A * (1-t)^3 B * 3t(1-t)^2 C * 3t^2(1-t) D * t^3 $\endgroup$ – jane Aug 3 '15 at 5:30
  • $\begingroup$ I understand what does formula for... I just don't get where I would get the "t" (time), is that up to me? or is there a formula for that as well? $\endgroup$ – jane Aug 3 '15 at 5:31
  • $\begingroup$ and thanks for this site, I will read further, thanks a lot! $\endgroup$ – jane Aug 3 '15 at 5:31
  • $\begingroup$ and also, I don't get where the B and C point came from... $\endgroup$ – jane Aug 3 '15 at 5:33
  • $\begingroup$ T is a value you put in to get different points on the curve. A value of 0 is the start of the curve, a value of 1 is the end of the curve, numbers between 0 and 1 give you points in the middle. $\endgroup$ – Alan Wolfe Aug 3 '15 at 5:40

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