Obtain function or contour lines of a surface

Hello,

I have several models that I need to calculate the amount of support required for 3D printing without using slicers.

I was thinking of calculating this using the function for the surface of the model i.e. f(x,y) or using.showing the contour lines on the model's surface.

I was wondering if it is possible to obtain the function for the surface i.e. function for a sphere is F(x,y) = +-sqrt(1−x^(2)−y^(2)). 

I am not sure that obtaining the function for any arbitrary surface is feasible or practical, so I figured that obtaining the contour lines of a surface could be easier. Is there a way to do this?

Any help would be greatly appreciated. Thank you.