[Algorithms] Sampling vs fitting values over vertices

[pete d. <pb...@po...>]

Our engine (I presume, like many others) stores some lighting/misc data 
per mesh vertex that would really be best stored in a texture.  This 
works reasonably well and in itself doesn't bother me terribly, but the 
fact that we sample the values at the vertex itself does.  The 
artifacts, ie the occasional dark tri due to occlusion at the verts 
being much darker than the average over the face, are something our 
artists have gotten used to painting out.  But I'd hope we could give 
much better baseline results.

So instead of simply sampling at vertices, I was planning on generating 
samples on each face (probably somewhat uniformly over the outside area 
of the mesh) and fitting (least squares) for the vertex values.  Ie try 
to minimize the actual deviation of the interpolated values over the 
face from what they should be, instead of simply ignoring the fact that 
they'll be interpolated..  And in additional to accuracy, it should let 
us handle hard edges, doublesided tris and a few more situations more 
accurately than they are now.

I presume people have done this before, so before trying it out I 
thought I'd ask if anyone had positive results, rules of thumb about how 
dense data needs to be sampled to generate good results in most cases, 
if applying a similar scheme to additionally generate gradients wrt u&v 
gives compelling improvements, etc.  Searching on the web/archive didn't 
really find too much (besides D3DX PRT methods that don't say how they 
work, and still require a texture thus an atlas/usable parameterization, 
which I don't really want to deal with).  Thanks for any input!

Pete