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Checking whether a curve is a parabola or not

  1. Jan 25, 2010 #1
    Hi everyone,

    I'm generating some hypar surfaces for a structure through parametric design techniques. In order to assess their structural abilities, I am finding their cross section curves and would like to check whether they are parabolas or not.

    So, in 3d space, (x,y,z) I have a curve - I can find the coordinates of n number of points along it. I cannot necessarily find the vertex as I do not know what portion of a parabola the curve might be .. My question is, can anyone help me figure out a way to check whether the curve itself is a parabola (or part of a parabola) or not?

  2. jcsd
  3. Jan 25, 2010 #2


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    Homework Helper

    Since you are dealing with a cross section, the implication is that the points are planar, which means you should be able to express the points as x-y coordinates. Once you have that, I can think of a couple of approaches:

    1. Use 3 of the points (e.g. 2 end points and a middle) to determine the equation of a parabola that passes through the 3 points, then test the n-3 points to see how close they are to the analytical curve.

    2. Slightly different from #1, perform least squares analysis on the n points to determine the coefficients of a 2nd order polynomial fitting function. The value of residual will give you can idea of how close the points fit a parabola.

    In both cases, a visual plot is always helpful.
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