since it’s light, there is no occlusion, so just stack the contribution from all the ellipsoids together and you’re done.
and then I scratched my head at how you can possibly do a credible rendering of any real scene without occlusion, contemplated that the images in the paper absolutely had occluded objects, and then read a bit more and figured it out:
Each ellipsoid has a “density,” which is a single number indicating the degree to which it absorbs light coming from behind it. And this formulation allows the integral along a path from infinity to the camera to be exactly evaluated. So there is occlusion! It just happens to work correctly even when ellipsoids overlap.
[0] It’s slightly more complicated, but not much. The raw density scales a term in the integral, but this results in a poorly behaved gradient, so the trained parameter is more or less the opacity when looking through the center of the ellipsoid through the shortest axis.
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I read this:
and then I scratched my head at how you can possibly do a credible rendering of any real scene without occlusion, contemplated that the images in the paper absolutely had occluded objects, and then read a bit more and figured it out:
Each ellipsoid has a “density,” which is a single number indicating the degree to which it absorbs light coming from behind it. And this formulation allows the integral along a path from infinity to the camera to be exactly evaluated. So there is occlusion! It just happens to work correctly even when ellipsoids overlap.
[0] It’s slightly more complicated, but not much. The raw density scales a term in the integral, but this results in a poorly behaved gradient, so the trained parameter is more or less the opacity when looking through the center of the ellipsoid through the shortest axis.