I am interested in an art project in which I am producing mosaics to cover the interior surface of a parabolic dome. The interior surface can be modeled by rotating a quadratic curve around the y-axis. (e.g., f(x)=h-x^2/k)
I need a 2D map this 3D space, to lay out the mosaics. I am thinking that I could estimate this area using the circumference of the dome at a fixed interval as it varies. But if there is a more elegant solution, I want to learn how to do it.
I just need to be pointed in the right direction...after reading lots of stuff that is over my head, I am thinking that a "conformal mapping" in what I am after (as opposed to a projection?). However, lots of the notation on this site is really difficult for me to understand.
Thanks for any help, and for keeping it relatively simple.