What is the different between ESM and CESM?


Does CESM use a logarithmic function?
logarithmic :

exponential:

I think this should have the same effect.

Hello! You can see the functions used to compute ESM and CESM in shadowsFragmentFunctions.fx:

  • ESM : float esm = 1.0 - clamp(exp(min(87., depthScale * shadowPixelDepth)) * shadowMapSample, 0., 1. - darkness);
  • CESM: float esm = clamp(exp(min(87., -depthScale * (shadowPixelDepth - shadowMapSample))), darkness, 1.);

They look pretty similar to one another at a glance, but once you plot the values according to the shadowMapSample value, they look pretty different (for simplicity, I substituted depthScale and shadowPixelDepth for 1.0, and darkness for 0.0):

ESM is f1, CESM is f2. The link to the plots is here: Graphtoy

@sebavan can complement with anything I missed :smiley:

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I’m a little confused.
ESM core formula:
image
But we use this formula:
ESM : float esm = 1.0 - clamp(exp(min(87., depthScale * shadowPixelDepth)) * shadowMapSample, 0., 1. - darkness);
It make the shadowMapSample without exp.Why can we omit the exponent calculation?

Seb will be the best person to answer but he’s out of office for a few days so he may take a bit to respond :slight_smile:

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Okay~Thanks!

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No, the shadowMapSample is generated with the exp, see:

As explained in this thread, we are doing e^(-c*(z-d)) and not e^(-c*(d-z)), that’s why we need to do visibility=1-e^(-c*(z-d)) in the end.

If you want to use the formula from the original paper (which are the ones you quote), you should use CESM and not ESM in Babylon.js.

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