Helicoid transformation

hi everyone,

I've just started with programming and made ​​this little Helicoid exercise. What I'm more interested in is to transform this geometry into a catenoid as shown here: http://mathworld.wolfram.com/Helicoid.html.

To be more precise, I'm not quite clear how to apply this equation to the helicoid and integrate it into my code:

where  corresponds to a helicoid and  to a catenoid.

I've made ​​some attempts not worth to be shown here. Maybe somebody can help me with a pseudocode or a simple description how to start solving this classic geometric transformation.

Thanks, Sebastian