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Bézier Curves

  1. Jan 17, 2008 #1
    Hi, I'm programming a visual implimentation of a bezier curve for a coursework. It would be beneficial for me to find the tangent at any point t on the curve. I can calculate the position of a point t, and so can hash the problem somewhat by finding the gradient between t+- a small value, but I was hoping for a more mathmatically accurate method.

    So I have the basic equation

    nCr * t^r * (1-t)^(n-r) * Vector for point

    which I tried to differentiate to...

    nCr * r * t^(r-1) * -(n-r) * (1-t) * Vector for point


    where
    t is progress along curve (between 0 and 1)
    n is the number of control points
    r is which iteration of the list of points we're on.


    is this correct? I'm not sure if it's the programming or the maths that are causing the problem.
     
  2. jcsd
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