This is also an implicit surface, right? (Because the function of the surface is given.) The reason why it is difficult to perform inside/outside tests is the shape. If the shape is described in explicit form (such as a triangle mesh), it will be more difficult to perform inside/outside tests.

@Anne,

Actually, this is an explicit description of the surface, because for every point (u,v) the function f(u,v) produces a point on the surface. Compare with the implicit description of the torus on this slide, where one cannot immediately find points (x,y,z) on the torus. In other words, the difficulty of performing inside/outside tests doesn't have to do with the "complexity" of the shape; rather, just the way it is expressed (implicitly or explicitly). Hope that helps,

Keenan

Ohhhh, so an explicit description means we can give in any input to the function and we get a point (hopefully) and impicit is having the relation which points in space should satisfy but necessarily all inputs to the relation won't.

I thought explicit description was just a bunch of samples of surface as a list, this is obviously not the case.

Exactly!