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Nick,
I myself used to interpolate gradients over the edge, but never got rid of the overflow/underflow that resulted from roundoff errors(?).
Then I changed the way I calculate subtexel "corrected" gradients, I did not interpolate them at all. I calculated the constant dudx and dudy ( for u coordinate, for example ) for the whole triagle. Ok, so far this is old-skool, and errors can result still.
If you know constant gradients over X and Y axis, and pixel's coordinate ( in integer!!! ), you can do this:
u_at_origin + ix * dudx + iy * dudy;
And you get -perfect- solution, I'm not sure if this is best possible, but I haven't got under/overflows ever since.
Now we see obvious optimization:
iy * dudy is simple adder, for each scanline you can actually replace it with:
foo += dudy;
If you initialize the foo with:
foo = dudy * iy_at_top;
You get interpolation. You still need to do the ix*dudx calculation, and add, but those can be done in any precision you like: float, fixedpoint.. ( float if you want to do subaffine perspective correction but that's another story ;-)
So we're left with multiply+add per scaline per gradient, this isn't so bad as you'd be doing this anyway if you did "subtexel" adjustment "manually", heh, now we correcting automatically to center of pixel ( or anywhere you like ), without even thinking "subpixels"-- it just happens when it's done right from the square one.
.. hope my explanation wasn't too vague, it should be fairly clear if read it more than once.
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