Question: What is the internal basis of the "generatePixelAreaLookup" function

[OliverXH]

I have been reading the source code of this repo recently and have some questions about the function used to generate probePixelAreaLookup data. What is the internal basis of the generatePixelAreaLookup function?

export function generatePixelAreaLookup(probeTargetSize: number) {
  const probePixelCount = probeTargetSize * probeTargetSize;
  const lookup = new Array(probePixelCount) as number[];

  const probePixelBias = 0.5 / probeTargetSize;

  for (let py = 0; py < probeTargetSize; py += 1) {
    // compute offset from center (with a bias for target pixel size)
    const dy = py / probeTargetSize - 0.5 + probePixelBias;

    for (let px = 0; px < probeTargetSize; px += 1) {
      // compute offset from center (with a bias for target pixel size)
      const dx = px / probeTargetSize - 0.5 + probePixelBias;

      // compute multiplier as affected by inclination of corresponding ray
      const span = Math.hypot(dx * 2, dy * 2);
      const hypo = Math.hypot(span, 1);
      const area = 1 / hypo;

      lookup[py * probeTargetSize + px] = area;
    }
  }

  return lookup;
}

Is there any calculation basis?

[unframework]

Hi Oliver, this function computes the multiplier for each pixel of the light probe half-cube (well, of each side of the half-cube). The pixels near corners/edges of the cube are weighted less than center pixels in the resulting average. In other words, this is mapping cube pixels onto a sphere before combining them into a final sum. Actual mathematics here are very much approximated, I actually did not test this for physical precision or anything - the aim of the whole project is to be a quick convincing hack instead of a full mathematically correct solution. Hope this helps!

[OliverXH]

@unframework
Thank you for your answer
I drew the following figure based on the source code and your answer, which is very useful for me to understand how it works:

This also makes me understand the following program:

const area = probePixelAreaLookup[py * probeTargetSize + px];

r += area * probeData[i];
g += area * probeData[i + 1];
b += area * probeData[i + 2];

[unframework]

Yep that describes it nicely, thanks for the diagram!