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Math Help - Need help to figure out a function for a curve

  1. #1
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    Need help to figure out a function for a curve

    I encountered this problem when programming movement and rotation of a sprite. it's a train moving on a parabola curve. I figured out the movement function but have trouble on the rotation.
    rotation is depend on the y variable of the movement function, let's call it variable a.

    have a few points from placing the sprite at right position and rotation.

    (a, r) // a is from y value on the parabola, r is the rotation value(the value i seek from the unknown function) r is dependent on y value;
    will be (x,y) on a xy plane


    (7, 0)
    (43, -26.31)
    (85, -31.4)
    (189, -34.55)
    (351, -38.5)
    (493, -40.82)
    (740, -44.87)

    I need to find the rotation function that takes a as an input.
    from the look of it, the graph look like r=a^something, where something < 1;
    Thank advance for any help from you guys.
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  2. #2
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    Re: Need help to figure out a function for a curve

    Hi !

    it's not sure that it is a parabola. It could also be an hypernola with non-orthogonal asymptotes.
    So, I suggest a quadratic curve regression with least squares fitting.
    After computing the coefficients for the general equation of the quadratic curve, it is easy to identify a parabola or an hyperbola or etc. Then, the center, the axis,... can be determined and asympotes as well if they are some.
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