Grasshopper

generative modeling for Rhino

# Parabola

OK, so I'm an Architect with a decent but certainly not coplete set of mathematical skills...
I need to do a parabola from 3 given points in grasshopper.
Can anybody help me with hints, or even definition files?!
(I have done a google search, but to be onest, the discussions going on at PhysicsForum.com is a bit over my head!)
Help most appreciated!

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I'm afraid that my mathematical understanding wasn't enough to grasp the explanation at Mathworld - http://mathworld.wolfram.com/Parabola.html of three points determining a parabola.

But I think the first part of the solution is given here - http://mathforum.org/library/drmath/view/55454.html
hehe.. thanks for answering, that explanation was helpfull, even though my reply to the end question; if I know what to do with three equations in three unknowns.. is no, not really ;-)
I feel like I should have paid more attention in HighSchool Math lessons...
Anybody here who understands this math?!
There seems to be a possibility that even if we do figure out the math, that you still cannot construct your parabola from only three points.
This picture is from - http://mathworld.wolfram.com/Parabola.html

And according to Dr. Math - http://mathforum.org/library/drmath/view/53228.html you'll need 4 points to determine a parabola.

As far as I understand, 3 points is enough as long as we know the centerline of the parabola. I my case the 3 points are floating points, and the parabola axis are given by a line created from the top point to the centroid of the two other points.
So I have the grey points, and from them create the blue point and centerline. Now I would like to draw the parabola through thegrey points.

If you have the time to convert Java to VB the code is all here
Thats exactly what I need.. However, given my current knowledge of Java and VB, I don't think I have that kind of time...
Its seems like a complicated script, is it hard to convert into a grasshopper VB script you think?!
I'd try to get a Java > VB converter to do the brunt of the work and then sort out the code for the Open Nurbs classes afterwards.
That's great, knowing both the vertex and one point will be enough.

The parabola can be written as y=a(x-h)^2+k where the vertex is given by (h,k)

Attaching a definition which I hope is correct. Using the values h and k from the vertex and x,y from the known point we first find a. Then using the equation above to plot the curve.

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Yay... That seems to work like a treat!
You obviously remember the classic virtues of math a bit better tham me!...

Thanks!
Hi guys,
Would you know how to make a three dimensionnal parabola like in the image hereafter? I have a set of points generated from a free-form surbs surface and would like to adapt it to parabolic profiles.
Many thanks,
Arthur

If I wanted this parabola to open in the 'Z' direction, how would I do that using this system?

Here it is in the XZ plane if that's what you mean.  I just disconnected the y point inputs and reconnected to the corresponding z inputs.

Chris

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