20161023 - Sphere Tracing AA

General idea for anti-aliasing with sphere tracing. The end result of this would be a very analog film feeling image with grain...

Ray Directions - Shoot one ray per pixel and use a good temporally changing low discrepancy sampling for ray direction.

First Hit - Trace forward until 2D projected distance to surface is within pixel diameter. I'm using diameter here because one wants a thin feature to show up as partial coverage across at least 2 pixels (to get good AA). Likely this distance needs a tuning knob, best might be half between pixel radius and diameter, depends on visual preference.

Coverage - Compute pixel coverage and store coverage with ray output. This part I'm speculating on and would need to try to see what works. Initial idea: step one more time through the surface, then take the last 2 distance samplings and try to estimate the actual surface, sample the distance function at the estimated surface, take this final distance as "coverage" (on surface = full coverage, reduce coverage as distance increases). Exact coverage isn't as important has having coverage approach zero as ray passes a surface without getting near enough. Error on surfaces will just show up as temporal grain, which is visually pleasing.

Reconstruction - For each pixel take nearest 11 rays. Take a weighted sum of ray colors where weight is F(DistanceFromRayToPixelCenter) * Coverage then divide by sum of weight. The F() function is the filter kernel, where fastest (but not highest quality) is the Gaussian, exp2(-scale*dst*dst). Could also do disk average (return 1.0 under a given radius, and some smooth fall-off outside that radius). Note DistanceFromRayToPixelCenter is constantly changing temporally due to low discrepancy sampling. Also nearest 11 rays is a fixed pattern,

   XXX
  XXOXX <-- 11 sample pattern
   XXX

Grain - After reconstruction add some grain to help mask the temporally changing sampling pattern.