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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!