Parameterise the surface of the torus generated by rotating

Parameterise the surface of the torus generated by rotating the circle given by (x - b)^2 +z^2 = a^2 on the xz - plane around the z - axis (with 0

Solution

Answer :

A circle with centered at (b,0) and of radius a in the plane XZ - has the parametric equation :

x = acos + b and z = asin with in the range [ 0 , 2 ] over the circle.

Now if we rotate the plane xz around z by x xcos + b , y xsin with    in the interval [ 0 , 2 ]

For a full rotation , x = (acos()+b)cos()

                            y = (acos()+b)sin(),

                    and z= asin()