Checking whether a curve is a parabola or not

[adelz]

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?

Thanks!

 

[hotvette]

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.