How can I generate a 3D torus taking a function as the torus shape?

I'd like to graph a 3d surface with a torus like aspect from this function

This function generates the top half of an ellipse, I thought of an approach of revolving this function around the y-axis and then doing the same process with the same function multiplied by -1, but, I wouldn't know how to plot this inside Matlab.

Thanks.

[Dyuman Joshi]

You need 2 ellipses to build a torus.

[Marco Cordero]

Wouldn't it be possible with the provided function? At the end, it's one half of an ellipse, just make it negative to obtain the other half and then displace these halfs to have the additional ellipse

[Dyuman Joshi]

Please refer to this link - https://en.wikipedia.org/wiki/File:Ring_Torus_to_Degenerate_Torus_(Short).gif

You can see that there are two rings (red color ones) that define a torus.

Generally, the inner ring, the one that revolves around, is a circle. You can use a non-circular ellipse in place of it.

So, you can use the same ellipse for both the rings, but the outcome might not be aesthetic (for the lack of a better word).

Answer 1

[KSSV]

R1 = 3 ;
R2 = 1 ;

 u = linspace(0,2*pi-eps) ;
 v = linspace(0,2*pi-eps) ;

 [u,v] = meshgrid(u,v) ;

 X = (R1+R2*cos(v)).*cos(u) ;
 Y = (R1+R2*cos(v)).*sin(u) ;
 Z  = R2*sin(v) ;

 surf(X,Y,Z)
 axis equal