General equation of a torus.

[BigMoosie]

I have worked out the formula for plotting a torus but I cannot seem to simplify it into a general equation. This is what I have got:

 

[math](a-\sqrt{x^2 + y^2})^2 + z^2 = b^2[/math]

 

Where [math]a[/math] is the radius from the origin to the center of the pipe and [math]b[/math] is the radius from the center of the pipe to the surface.

 

Any attempt I make to remove the square root just complicates things even more.

[matt grime]

did you think of googling for "equation of a torus"? cos it'll show you are correct and that is about as simple as it gets in cartesian co-ords. but then there is no reason why it should be simple is there?

[DQW]

double-post; deleted

[DQW]

Why do you want to eliminate the square root ? I can't imagine that the square root causes a problem with the plotting ! Nevertheless, you know you can exliminate the sqrt by collecting terms and squareing - only you'll end up with something that has 16 terms !

 

You could, alternatively, use the parametric form :

 

[math]x = (R + rcos \theta) cos \phi [/math]

[math]y = (R + rcos \theta) sin \phi [/math]

[math]z = r sin \phi [/math]