Finding the Control Point in a bezier curve

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.)

Answer

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/

Attribution
Source : Link , Question Author : jane , Answer Author : Alan Wolfe

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