Understanding Bezier curve equations

Thread Starter

zulfi100

Joined Jun 7, 2012
656
Hi,
plz guide me about the eq which i have shown in the post#1. I have provided the solution in post #7.
BEZk,n(u) are the Bernstein polynomials.

BEZk,n(u) = C(n,k) * (u) (to the power k) * (1-u) (to the power n-k)
where C(n,k) are the binomial coefficients.

I have also formed the curve which is attached.

Zulfi.
 

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WBahn

Joined Mar 31, 2012
29,976
Thanks. I see the curve. Thanks for your guidance. I would try to draw the curve if possible. But now how you discovered the control point? Where should i put the second control point (i.e on the same side adjacent to C1 or on the opposite side of C1??)?

Also the question related to my solution remains unsolved (i.e post# 7). I have already specified what i know. I would try to find a link for it.

Zulfi.
Where you put the control points will depend on what you are trying to achieve. The line leaves the first point tangent to the line between that first point and the first control point. It arrives at the final point tangent to the line between the final control point and the final point. Beyond that the relationships get more complicated quite quickly.
 

WBahn

Joined Mar 31, 2012
29,976
Hi,
plz guide me about the eq which i have shown in the slide#1. I have provided the solution in slide #7.
BEZk,n(u) are the Bernstein polynomials.

BEZk,n(u) = C(n,k) * (u) (to the power k) * (1-u) (to the power n-k)
where C(n,k) are the binomial coefficients.

I have also formed the curve which is attached.

Zulfi.
Hopefully someone else can help you on this. I have never heard of Bernstein polynomials and I have neither the time nor the desire to learn about them right now (or in the foreseeable future).

But my guess is that if YOU want to understand those equations, then you would be well-advised to make sure that you know what they are and what is special about them.

Good luck.
 

Thread Starter

zulfi100

Joined Jun 7, 2012
656
Hi,
Thanks for tranferring this important knowledge. However i still need guidance for Bezeir equations which i have shown in my Post#1 and provided solution in Post#7. Somebody plz guide me.

Zulfi.
 

nsaspook

Joined Aug 27, 2009
13,079
Hi,
Thanks for tranferring this important knowledge. However i still need guidance for Bezeir equations which i have shown in my Post#1 and provided solution in Post#7. Somebody plz guide me.

Zulfi.
I think the questions you have are really about the math related to De Casteljau's algorithm being used to generate curve approximations using line segments (usable with standard frame-buffer libraries) with the Bezier control points instead of a just a series of pixels.

This is about a good as I could find to help with your questions. (much more that I know about them) LATER...
http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/
http://pomax.github.io/bezierinfo/
 
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