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!

1 Like

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
y(u,v)= b squared (1+u
z(u,v)= c

and i don’t know how to “translate” a and b. I (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! :smiley::smiley::smiley:

sqrt is Square Root, not square. To square something called a you either write a*a, , 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)


a² * (1 + u²) * Cos(v)
1 Like

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
Now i m try to do what you say!
Thanks so much!:grinning:

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)
1 Like

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… (10.2 KB)

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

1 Like

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… :smiley:

and the new file is here,
Thanks so much! (10.0 KB)

Why mess around with interpolating points when you can generate a mathematically exact hyperboloid using NURBS? :slightly_smiling_face:
Check out this article:

1 Like

1 Like

Have a look at the attachment… (9.1 KB)


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: (10.5 KB)
(edited from HS_Kim’s answer)

1 Like

Hi! Thanks so much! :smiley:

Hi Joseph!
Thanks so much! As i can, i try it! :smiley:

Thanks so much@:
I try it as soon as i can! :smiley: