I agree that it's visually displeasing, but it's very easy to actually read and understand.

The only reason I was able to quickly understand your beautifully-aligned code was because I had read the logic in the previous block, which is stupidly-easy to parse.

I also (like many others) shun the use of nested ternary operators. Probably because I'm used to dealing with PHP's straight-up broken implementation.

Further, I'd have split the side being determined from the sides array, as it's rather mentally taxing to figure out the increment at the end:

  if (dot < -LIGHT_CLIP_EPSILON) {
    side = SIDE_BACK;
  } else if ...

  sides[i] = side;
  counts[side]++;