# Create an Elliptic Hyperboloid from the matematic formula

Sorry! I m not able to try to write the formula because i don’t know how to write with the computer the symbol “racine carrée” that we have here, as you can see here on the formula i download in jpeg. Can you please help me? Thanks so much!

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Thanks so much!
Here, it is the file, i try to do the formula, but it seems i made mistakes.
I know that the z: cv, cu, does’nt have input and output, but i tried to do input, and output, and nothing appears. Here, i have something… but wrong i know.
Other thing is that formula is:
x(u,v)= a squared (1+u
u)cos(v)
y(u,v)= b squared (1+u
u)sin(v)
z(u,v)= c
u

and i don’t know how to “translate” a and b. I dEllipticHyperbol.gh (10.9 KB)
I did like it would be “1”, but shure it’s more complex…
So, thanks so much if you can’t help me!   `sqrt` is Square Root, not square. To square something called `a` you either write `a*a`, `a²`, `a^2` or `Pow(a, 2)`.

If your expression need to access values `u`, `v`, and `a`, then your expression object needs to have those three inputs. You can add (and remove) inputs by zooming in on the expression component and clicking on the (+) signs. You can rename inputs via their context menu. So add a third input called `a` to your expression, and type:

``````a * a * (1 + u * u) * Cos(v)
``````

or

``````a² * (1 + u²) * Cos(v)
``````
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Hi David!
Thanks so much!
The formula, as we can see on my first post here is:
x(u,v)= a squared root of (1+u*u)cos(v)
y(u,v)= b squared root of (1+u
u)sin(v)
z(u,v)=c
u
Now i m try to do what you say!
Thanks so much! I didn’t read all the way back to the beginning, I just responded to your last entry which read ‘squared’ not ‘square root’.

The correct GH way of writing the equation from your mathworld screenshot is:

``````a * Sqrt(1 + u * u) * Cos(v)
``````
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Hi David!
Thanks so much!
Now, i tried to do what i think it was good, but it’s wrong… Here you have the screenshot:

And the new file i modified… but it 's wrong… EllipticHyperbol2.gh (10.2 KB)

Your expression uses `c`, but you have no input for that variable.

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Hi David!
thanks so much!

Now i think it’s better… but i think it’s not the result i should have, it’s not an elliptic hyperboloide, and i have only points… but better… and the new file is here,
Thanks so much! EllipticHyperbol2.gh (10.0 KB)

Why mess around with interpolating points when you can generate a mathematically exact hyperboloid using NURBS? http://www.danieldavis.com/how-to-draw-a-hyperboloid/

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One nice thing to realise about the formula is that for any given parameter u, the Z coordinate is fixed and the X and Y coordinates describe an ellipse of the form

x = a'*cos(v)
y = b'*sin(v)

This allows you to factor out the variable v entirely, and end up with a smoother and simpler surface:

EllipticHyperbol3.gh (10.5 KB)

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Hi! Thanks so much! Hi Joseph!
Thanks so much! As i can, i try it! Hi!
Thanks so much@:
HS_Kim
Joseph_Oster
qythium
I try it as soon as i can! 