Parametric Equation of Torus: Deriving Solutions

[dpa]

Homework Statement

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.

Homework Equations

* 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:
<sinu+a, cosu>

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
<asin∅,acosb>.

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.

Thank You.

 

[LCKurtz]

Here's a link. Google is your friend:

https://www.math.duke.edu//education/ccp/materials/mvcalc/parasurfs/para1.html

 

[dpa]

Thank You.