2d-equations mapped on uv-coordinate-system of surface

hi there...
how would i approach an asymmetrical triangular mesh development based on surfaces?...
i know i can analyze existing surfaces giving me single or multiple uv-points on a particular surface which could then be used for further geometry development... but my particular interest is: is it possible to use a list of points as input instead or even algorithmic approaches with the use of 2d-equations that map onto the uv-coordinate-system of that particular surface? can anyone give me a hint?
greetings
ante