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I'd like to be able to texture map images that are stored as Adobe Illustrator-compatible vector images which get rasterized on the fly during render time as necessary by Maxwell.

Very cool wish!
Yes, that would be great.
Currently for all sorts of repeating Displacement-Patterns with smooth gradients (16Bit) one needs to use Photoshop to create them.
While Photoshop is pretty poor with Vector-Creation it afaik the only App which converts Vectors to 16 Bit Images.

If Maxwell would read Vectors from all sorts of Packages in formats like .ai or .svg the creation of repeating high quality maps was a lot easier,
especially as in Illustrator CS6 they finally established an interactive way to define patterns.
Maps could easily get changed and showed updated in Fire.

And it would be nice to be able to fly the camera very close to a texture mapped object and not have to use a high rez texture and not see the texture map reveal its soft, pixely edges.

Would be especially good for use in the material layer masks that layer one material over another.

I can see a huge slowdown coming... while traditional textures just access a memory location and maybe interpolate, a vecor image would need to be rendered (at least in part) for each texel. Vectors would just trade speed for memory.

Thanks for the technical insight Ha_Loe!
At least from my side the wish was only to read in vector which by the Engine got converted to Bitmaps in the most efficient way
at the point in time which makes most of sense. Heck - maybe this could even happen in a Ptex-fashion which gives Edges more Texture-Space
and so could optimize their appearance...

Ha_Loe wrote:I can see a huge slowdown coming... while traditional textures just access a memory location and maybe interpolate, a vecor image would need to be rendered (at least in part) for each texel. Vectors would just trade speed for memory.

There's an easy solution for you in that case: don't use them.

Personally I'd be tempted to use it in cases where a big change in scale during an animation takes me quite close to an object over time.