>  That's not always possible. Simple example: A torus composed of quads,
> and a rectangular texture image wrapped onto its surface. The texture will
> be distorted at the places where the quads are non-rectangular.

True, but if you use enough quads that your torus looks like a torus and not 
like a jaggedy square wheel the distortion is going to be minimal.  And 
anyway, won't you have exactly the same problem using triangles instead of 
quads - the renderer can only interpolate linearly and a rectangular texture 
on a torus needs a non-linear interpolation to be correct.

>  I suppose you could tansform the texture image so that it matches the
> shape of the quads at each point. It would make the texture irregular and
> larger, but I suppose it might work. OTOH, if you ever decide to change
> the resolution of your torus (ie. change the number of quads it's composed
> of), you'll have to re-calculate the texture as well, which might not be
> practical.

In most modellers I've seen you apply your texture in certain ways to the 
mesh and the modeller automatically calculates the texture coordinates at 
each vertex for you, so you don't have to concern yourself with making sure 
the textures are distortion free.

>  Perspective has nothing to do with what I'm talking about.

I mentioned it because it's the most common situation when you need to map a 
rectangular texture onto an often hugely non-rectangular quad, and it's 
important it looks right.

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