Modelling surfaces


I you have a mathematical description of a surface (that describes all the points on the surface), how would go about creating a polygonal approximation for that surface?

What are the mathematics behind this called? What terms are used? What keywords do you use when searching for information about this on the net?


You mean, curves like Bezier splines or curved surfaces with Bezier Patches? Search for “curved surfaces”.

If you have an implicit definition (like x^2 + y^2 + z^2 - r^2 = 0 for a sphere), try searching for “marching cubes.” It is a pretty decent way of drawing polygonal approximation of isosurfaces.

If you can massage your definition (of the form f(x, y, z) = 0) into a functional one
(like z = f(x, y)), that might be better because doing the spline approximation thing(by sampling the function domain) is quite a bit simpler/faster.