What is the equation of the Parabola plotted by Rhino?

When I plot y=x^2 from an external file of data points I get a different curve when compared to what is drawn if I use the Rhino Parabola command (either form), which seems to draw a more open curve, something like y=2x^2.
I can then drag the endpoints of the parabola to match my plotted y=x^2 curve, but I’d rather specify it directly.

  1. What am I missing here?
  2. What is the equation of the Parabola plotted by Rhino?
  3. Can this command plot the y=x^2 curve?

Every year High School math gets further away from me, so admittedly, that might be my problem.
Thanks for your help,
Ian J

I’m curious how do you “plot” the supposedly parabola points from file in Rhino? Interpolation? ControlPointsCurve?

Hello - y=x^2 is an equation for a particlar parabola, not all of them… If you have a set of X coordinates and would like the points with Y according to y=x^2, it is certainly easy enough to get these in a script.


The Rhino AddPoint command does that. I first create a text file of points to plot, like:

-5, 25, 0
-4.99, 24.9001, 0
-4.98, 24.8004, 0

Then I use a Rhino script to load the text file of data (using LoadScript, RunScript) and that will plot them in the Rhino workspace.

Hey Pascal,
Thanks for your reply. I still may not be understanding something. The general form of the equation for a parabola, as I understand it, is y = ax2 + bx + c (and there are other forms this relationship can be specified.)
With a and b = 1, and c = 0, you would get a particular parabola. The curve that the Rhino Parabola draws also seems like a particular parabola to me, only one that has some value for “a”.
What I’m not getting in what you said is how the parabola drawn by the Rhino command is any less a particular parabolic equation? How is it somehow “all of them”?
I did use a script to plot a y=x^2 parabola from points, but I was hoping there was a Rhino command that could be supplied values that would create the nurbs curve equivalent to that same equation.
From what you said, I gather Rhino does not provide that command or functionality.
Thanks for your help,
Ian J.

Hi Ian -

Yeah, that is what I meant… I don’t, off hand, see how to translate the inputs for Rhino’s command to get a particular constant

y = 1/4p*x^2

may help, where p = the distance from vertex to the focus, since you do get to specify that distance in Rhino’s command.


Hi Pascal,
OK, I was able to use the Parabola - Vertex, Focus command successfully to duplicate the particular parabolic equation y=x^2.
Choosing a vertex at (0,0) and a focus at (0, 0.25) creates the same curve as y=x^2.
I must have been confused, because I thought I had already tried this.

In case this is helpful to anyone else:
The vertex form of a parabola equivalent to y=x^2 is:
y = a(x-h)^2 + k
The vertex will be at (h,k) and the focus at (h, k + 1/4a) (“a” in this case is 1)
If the vertex is at (0,0), then the focus is (0, 0 + 0.25)

Thanks again, Pascal, for your assistance, it caused me to go back and work through this again.
Ian J.

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