# Thread: Elements of Bezeir Curve Equation

1. Hi,
I am studying about Bezeir Curve. I found following eq:
P(u) = Σ Pk BEZk,n (u)

I know that:
P(u) = Position vector which tells the path of curve between any two consecutive control points
Σ = Summation sign
Pk = control point position
BEZk,n = Bernstein polynomial having a binomial component multiplied by: uk * (1-u)m-k

I cant understand what is "u"?

Plz guide me about "u" and if i am wrong in understanding any component of this equation.

Zulfi.  2. Zulfi, please guide me, what is m?  3. I think u is the independent variable and it looks like m is the number of terms in the polynomial.  4. Hi,
Thanks for everybody who is trying to help me with this problem. I made a mistake. I checked the book and i found that i wrote something wrong. Following is not correct:
BEZk,n = Bernstein polynomial having a binomial component multiplied by: uk * (1-u)m-k
According to book:
BEZk,n (u) = C(n,k) uk (1-u) n-k
where C(n,k) are the binomial coefficients:
C(n,k) = n!/(k!(n-k)!)

I think u is the independent variable and it looks like m is the number of terms in the polynomial.
Thanks for your comments. I agree that its an independent variable because I saw it plotted along x-axis. According to book its value ranges: 0<= u <= 1. Both the Position vector and Bernstein polynomial has an argument of "u". Why?? Bernstein polynomial is a function but Position vector is not.

Zulfi.  5. Zulfi, I think that u is the distance between the control points. But that's just an educated guess as Bezeir curves are not my thing.   6. Hi,
I think you are right because book according to book:
Bezeir curve passes through the first and last control points
P(0) = P0
P(1) = pn

I have done an example for drawing line for generating first order Bezeir curve. In that case, for example if we have to draw a line between
P1 = (-1, 6) & C1= (9, 5) then P(0) = (-1,6) & P1(1) = (9,5) i.e the endpoints of line and P(0.2) , P(0.4), P(0.6) & P(0.8) can generate the intermediate coordinates of points for line.

Zulfi.  7. Hi,
The Question is:
Q of Bezeir Curve.jpg

and the solution is:
Sol of Bezeir Curve Prob.jpg

Zulfi.  8. Originally Posted by zak100 Hi,
I am studying about Bezeir Curve.
Minor nit: It's Bézier, not Bezeir. Named for the French engineer, Pierre Bézier.  9. Hi,
Thanks for the correction.

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