Hah! I eat torii for breakfast!  

Since a torus is just a circle seen in the x-z plane (I'm assuming you
pick on y because you're taking that as the main axis), the formula
ought to be 

     (r-A)^2 + y^2 = B^2

where A is the major radius (origin to the midline of the curved pipe),
B is the minor radius (radius of the cross section of the pipe), and 

     r^2 = x^2 + z^2



You want it for y(x,z)?   Easy.

    y(x,z) = +- sqrt( B^2 - (r-A)^2 )

where you plug in

    r = sqrt( x^2 + z^2 ).


This formula for y(x,z) involves a square root, for which you take both
signs, so there are two values in most places where the torus exists,
one value only where r = A-B or r=B+A, and no real values where r<A-B or
r>A+B.  (Exercise for the student: if you plotted the imaginary values
of y(x,z) along y the y axis, what shape would you get?)





It would be fun to solve for x or z:

    x(y,z)  = +- sqrt( r^2 - z^2 )

where you plug in 

    r = A +- sqrt( B^2 - y^2 )
      
This formula for x(y,z) involve two square roots, giving four values in
the domain where y,z are in the torus (as projected onto the y-z plane).


Hope this helps.   I'll send you my bill <g>.

-- 
Daren Scot Wilson
Member, ACM
dar### [at] pipelinecom
www.newcolor.com
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