I am fairly sure both Max and Maya have the ability to do this, Max for sure at least.

It has several types of modeling methods.

Editable Mesh
Editable Poly
Editable Spline

Just off the top of my head. I dont have Max installed on this PC so Steve will probably let you know all of them.

Your Subdiv method uses the Editable Poly type, which is also what I use. I've never used any of the other methods but I think Editable Mesh is mainly for using Modifiers instead of slicing up your polys.

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That's quite a tough question. Not quite negative IOR but not far off.

Basically, yes in Max (and Maya) you can use several kinds of surfaces to model objects. However, you can only use one type on each object. You have to choose the best surface for your object and modelling strengths and go from there.

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I can't say I'm that well informed on all the mathematics behind the way 3d software
deals with surfaces but the way I understand it there are multiple methods to create surfaces like straight polygon modeling and subdivision, and spline or nurbs based modelling where curves are defined by mathematical expressions, but all of these will eventually be reduced to faces by the renderer. faces being the two adjacent triangles making up a polygon. if you had a patch (a spline cage with a surface modifier) that performed well in the viewport due to its simple control curves
with 100 interpolation steps it would actually represent the same load on your renderer as a meshsmoothed object with many iterations.
some renderers deal with geometry differently. I believe renderman has some sort of adaptive smoothing fuctionality, that is, objects get more iterations when the camera is closer to them. similarly vray displacement will subdivide the mesh more and more depending on your view.

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I didn't know that about vray displacement. Ahh, still teaching me after all these years.

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