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Thread: Elements of Bezeir Curve Equation

  1. #1 Elements of Bezeir Curve Equation 
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    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.
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  2. #2  
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    Zulfi, please guide me, what is m?
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  3. #3  
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    I think u is the independent variable and it looks like m is the number of terms in the polynomial.
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  4. #4  
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    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.
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  5. #5  
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    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.
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  6. #6  
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    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.

    Thanks for your help.

    Zulfi.
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  7. #7  
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    Hi,
    I have got a example which i downloaded from Internet:
    The Question is:
    Q of Bezeir Curve.jpg

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

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

    Zulfi.
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