I need to derive the prarametric equation of a certain torus. defined by a unit circle on xz plane with center (a,0) and revolving about z-axis.
* I don't know if this is relevant but here is something from wikipedia.
Surfaces of revolution give another important class of surfaces that can be easily parametrized. If the graph z = f(x), a ≤ x ≤ b is rotated about the z-axis then the resulting surface has a parametrization r(u,∅)=(ucos∅,usin∅,f(u)).
The Attempt at a Solution
I can derive the parametric equation of unit circle in xz plane which is given by:
I can also define the locus, (the path formed when constructing the torus, or let us say central circle of the torus), of the centre of the unit circle around Z axis in XY plane as above.
if we consider ∅ be the angle of revolution of center of unit circle about z axis, we have
I have no idea how to connect these two elements.
I would be infinitely obliged if someone could explain or provide a link for this.