# how to draw a hyperboloid?

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bsd on 25 Sep 2011
Commented: Benjamin Backus on 22 Jul 2020
Hai,
I need to draw a hyperboloid in matlab. How is it I could do it?
BSD
Fangjun Jiang on 25 Sep 2011
Then you need to explain what is hyperboloid and what you want to do. I can search for hyperboloid and it gives me lots of hits. For your benefit, barely mention hyperboloid in your question is not sufficient, right?
bsd on 25 Sep 2011
hyperboloid is a three dimensional representation of a hyperbola. Just like sphere, as sphere is a three dimensional and circle is two dimensional.
BSD

UJJWAL on 26 Sep 2011
Hi BSD,
I hope the following code will help. Reply back :-
clc;
clear all;
[X,Y,Z] = meshgrid(-10:0.5:10,-10:0.5:10,-10:0.5:10);
a=1;
b=1;
c=1;
V = X.^2/a^2 + Y.^2/b^2 - Z.^2/c^2;
p=patch(isosurface(X,Y,Z,V,1)); % This is the key step. It involves getting the part of the volume corresponding to the surface defined by the equation
set(p,'FaceColor','red','EdgeColor','none');
daspect([1 1 1])
view(3);
camlight
Hope This helps..
Happy To Help
UJJWAL
bsd on 28 Sep 2011
It gives both the upper and lower portion. But I need only the upper portion of the hyperboloid. How to do that? Looking for your reply.
BSD
UJJWAL on 28 Sep 2011
Hi BSD,
That is very easy as you just have to change the range of the x,y and z points you use in meshgrid
For getting the upper portion you just need to set z from 0:0.5:10
so in the above code just replace the meshgrid line with the following :-
[X,Y,Z] = meshgrid(-10:0.5:10,-10:0.5:10,0:0.5:10);
Hope This Helps
HAPPY TO HELP
UJJWAL

HAGOS EMAN on 18 Jun 2019

Fangjun Jiang on 25 Sep 2011
As long as you have the mathematical equation describing that hyperboloid, you should be able to generate some data and then draw it.
Take a unit sphere for example, the equation is x^2+y^2+z^2=1; If you carefully set the mesh grid for x and y, then you can calculate the corresponding value for z. Then you can use surf() to plot it.
MATLAB has the sphere() function. Here I am using it to generate the data first and then plot it. Running sphere alone can plot it too.
[x,y,z]=sphere;
surf(x,y,z)

Chaowei Chen on 25 Sep 2011
[x,y]=meshgrid(-10:10);
r_sq=x.^2+y.^2;
z=sqrt(r_sq+1);
surf(x,y,z)
Bud Kelly on 30 Mar 2018
This is very clever. Thank you, I will keep it for reference. I had thought that you needed to purchase Symbolic Math Toolbox to plot 3D explicit functions, but now I am encouraged. Thanks.
Benjamin Backus on 22 Jul 2020
That doesn't look like an ellipsoid to me. The 3rd line should rather be:
z=sqrt(200 - r_sq);
in order to have an ellipsoid of equation x^2 + y^2 + z^2 = 200 (200 because x and y have magnitude 10)