Christopher James Huff <cja### [at] earthlinknet> wrote:
> Right, it's not impossible

  I wouldn't say that. There are many problems which are not solvable
analytically. One classical example is modelling the orbits of a three-body
gravitational system: There's no analytical function which would give
you the location of a body at any given time. You have to calculate
it numerically (ie. approximating it iteratively).
  In the same way, not all functions/surfaces have an integral. If you
need to integrate over them, you need to make a numerical approximation.

  Thus, it might very well be impossible in the general case. (Which means
that there's no other solution but to approximate the real solution by
taking samples.)

  Another point is that it's probably not worth the efforts and resources.

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