Back in the early 90s I did a version of Bresenham's algorithm that would rasterize the hyperbolic curves that perspective-correct texture mapping required. It worked correctly though the technique of just doing a division every n pixels and linearly interpolating won out in the end, if I recall.
You could also avoid divisions entirely, while still keeping 100% correct perspective, by "rasterizing" the polygon following the line of constant Z.
You would save the divs, but then you would draw mostly outside the cache, so not a panacea, but for large surfaces it was noticeably nicer than divide-every-N-pixcels approximation.
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Perspective correct texture mapping has been solved for quite some time without excessive subdivision.
It was avoided in the Foley and Van Dam days because it requires a division per rasterized pixel, which was very slow in the late 80s.
Back in the early 90s I did a version of Bresenham's algorithm that would rasterize the hyperbolic curves that perspective-correct texture mapping required. It worked correctly though the technique of just doing a division every n pixels and linearly interpolating won out in the end, if I recall.
You could also avoid divisions entirely, while still keeping 100% correct perspective, by "rasterizing" the polygon following the line of constant Z. You would save the divs, but then you would draw mostly outside the cache, so not a panacea, but for large surfaces it was noticeably nicer than divide-every-N-pixcels approximation.