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Math Help - Fitting a Parabolic Curve to 3D Data

  1. #1
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    Fitting a Parabolic Curve to 3D Data

    Hi!

    I'm trying to write code to fit a parabolic curve to three points that are each three dimensional, but I'm not really understanding the math behind it and could use some help.

    Here are my three points:

    (-0.000461,0.003841, -0.001400)
    (0.000766, -0.002610, -0.001256)
    (0.005331, -0.015542, -0.011193)

    Could someone perhaps walk me through the process? (My math knowledge only extends up to BC calculus)
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  2. #2
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    Re: Fitting a Parabolic Curve to 3D Data

    Hello, lebronlin!

    I'm trying to write code to fit a parabolic curve to three points . . .
    We need more than three points.

    Unless there are more restrictions,
    . . there is an infinite number of such parabolas.

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  3. #3
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    Re: Fitting a Parabolic Curve to 3D Data

    Shouldn't there only be one parabola that fits these points? Since there is one plane for which these points all lie on and then couldn't I solve for the parabola in that plane
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  4. #4
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    Re: Fitting a Parabolic Curve to 3D Data

    Quote Originally Posted by lebronlin View Post
    Hi!

    I'm trying to write code to fit a parabolic curve to three points that are each three dimensional, but I'm not really understanding the math behind it and could use some help.

    Here are my three points:

    (-0.000461,0.003841, -0.001400)
    (0.000766, -0.002610, -0.001256)
    (0.005331, -0.015542, -0.011193)

    Could someone perhaps walk me through the process? (My math knowledge only extends up to BC calculus)
    1. A parabola belongs to the conic sections whose general equation is:

    Ax^2+Bxy+Cy^2+Dx+Ey+F=0

    2. If
    \Delta = \left| \begin{array}{ccc}A&\frac B2 & \frac D2 \\ \frac B2& C & \frac E2 \\ \frac D2 & \frac E2 & F\end{array} \right| \ne 0 ... and ... \delta = \left|\begin{array}{cc}A& \frac B2 \\ \frac B2&C\end{array}\right| = 0

    then the conic section is a parabola.

    3. From the general equation you can see that you need 6 points to determine the co-efficients A to F.
    That's what Soroban meant when he stated that we don't have enough informations.
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