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# 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
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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

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### Accepted Answer

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
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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

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### More Answers (3)

HAGOS EMAN on 18 Jun 2019
Thanking you all! Very helpful!
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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)
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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)
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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)

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