>> Ever heard of subdivision surfaces, Andrew?  You can get a perfectly 
>> round sphere out of a plain cube cage by specifying up to 5 iterations.
>
> Yes. But the resulting surface can only be controlled by the 8 original 
> cube corners. That's not much control.

It's very simple to add in more control points, every time you want more 
control you simple add in another point, this leaves you free to have 
certain areas with very few control points, and other areas with lots of 
control points, yet the result will be perfectly smooth.  For example when 
modelling a car the large flat roof might only need a handful of control 
points, but something around the wheel-arch might need many more to get the 
curvature correct.

Another benefit is that you can instantly switch between the level of 
subdivision, so you can have a 10 million triangle mesh for perfectly smooth 
rendering, or a 100k mesh for use in a game, both coming from exactly the 
same control points.

Watch this for a demo of it working (in BLender);

http://www.youtube.com/watch?v=ckOTl2GcS-E

around 0:47 you can see him editing the control points and the perfectly 
smooth surface is following.  This is how you design smooth triangle meshes, 
not point by point of the individual triangles!

> And yet, in all known editors, moving triangle corners around one at a 
> time is the only available editing operation...

Haha, do you *really* think that people haven't thought of a better way to 
edit triangle meshes? LOL

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