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!

Replies to This Discussion

Permalink Reply by Lars Renklint on June 23, 2009 at 2:34am

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

Permalink Reply by Jes Tonsgaard on June 23, 2009 at 3:06am

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?!

Permalink Reply by Lars Renklint on June 23, 2009 at 4:31am

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.

What about your three point, are they arbitrary, or do we know anything about them?

Permalink Reply by Jes Tonsgaard on June 23, 2009 at 4:44am

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.

Permalink Reply by Dirk Anderson on June 23, 2009 at 5:01am

If you have the time to convert Java to VB the code is all here

Permalink Reply by Jes Tonsgaard on June 23, 2009 at 5:05am

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?!

Permalink Reply by Dirk Anderson on June 23, 2009 at 5:11am

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.

Permalink Reply by Lars Renklint on June 24, 2009 at 7:16am

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.

Attachments:

parabola.ghx, 140 KB

Permalink Reply by Jes Tonsgaard on June 24, 2009 at 7:55am

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

Thanks!

Permalink Reply by Arthur Mamou-Mani on September 9, 2009 at 11:54am

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