Today, we're picking up right were we left last post. We are looking at building our irradiance map. As a refresher, the irradiance map is a low resolution cubemap where each texel corresponts to the cosine weighted integral of the incoming radiance across the hemisphere centered on that texel's direction. Given that description, it seems like a reasonable choice to build the irradiance map would be to solve the integral with importance sampling. Choose N samples from a cosine weighted distribution, and average them. And that, with N=1024 samples, is the approach chosen by the coding agent for writing our "initial implementation".
If you recall from the previous post, though, this came with a couple issues. First, we found siginificant aliasing artifacts in the cubemap. The following image is a capture of our irradiance cubemap, at it's current resolution of 32x32 texels per face, where I've highlighted some of the areas that show these aliasing artifacts.
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| Initial irradiance cube at 32x32 texels per face. Aliasing artifacts highlighted in yellow. |
We could mitigate this by increasing the number of samples, but this would increase the cost. And that is precisely the second issue: computing this low resolution irradiance map is already pretty expensive. To fix those two issues, we are going to completely rewrite the algorithm, and instead implement a version of Ramamoorthi's spherical harmonics irradiance. However, we're going to go one step further and fully resolve some of the math analitically, not so much for the speed up, but because it will make the implementation cleaner and simpler to understand.
