ZBias trouble with alternative cubemap shadow method

Question

I find two methods to produce cubemap for shadow both using the same geometry shader to draw each of the 6 faces. The first one writes in the depth buffer only and is used like this (really I thanks the guy having posted this code elsewhere (https://community.monogame.net/t/view-matrix-for-point-light-shadows/14548)):

float3 txDir =  Input.WPos.xyz - LightPos[2].xyz; 
float3 LtoP = normalize(txDir);
float Closet = -1;
int FIndex = 0;
for (int f = 0; f < 6; f++)
{
   float r = dot(LtoP, FDir[f]);
   if ( r > Closet ) 
   {
      Closet = r;
      FIndex = f;
   }
}
float4 LPos = mul(Input.WPos, LightViewProjCube[FIndex]);
LPos.z/=LPos.w;
D = txShadowCubeMap.Sample(samWrap, txDir).r;
Shadow = (D + 0.001f < LPos.z)?0:1;

as one can see you need some job to retrieve the correct face index and its light matrix to recalculate the position but this code works well.

the alternative solution from learngl tutorial use the same geometry shader but writes his own depth value in the depth buffer (I use a render target R16F in DX11 for this) in a 0..1 range via 1/farplane

float PS_CubeMap(PS_CUBEMAP_IN Input): SV_TARGET
{
   return length(Input.Pos.xyz - LightPos[2])*0.001f;//0.001 is 1/farplane 
}

then they use it like this:

float3 txDir =  Input.WPos.xyz - LightPos[2].xyz; //2nd pointlight (yellow)
D = txShadowCubeMap.Sample(samClamp,  txDir ).r;
if ( D < 1 ) //rendertarget red chanel cleared to 1. So 1 means nothing was drawn.
 Shadow = (length(txDir) > D*1000)?1:0;//*1000 restores the real distance

My problem here is that if the second method is 5-10% faster because less pixel operations it introduces a zbias problem for object being both shadow caster and receiver I can't figure out how to solve (see picture). I've tried to "push away" the distance value when generating the map or various additional bias when using the texture, or back/front cull for rendering the shadow, various sampler. No improvements. Of note all my matrices have the same 1/1000 near/farplane values. Is there something in this learngl code adaptation I'm missing?

Answer 1

Apparently using the distance from pixel to light and dividing by some arbitrary value to fit in the [0..1] range is not giving an accurate result. The solution I found to this is for a given pointlight to calculate the pixel to light distance and divide by the inverse of the radius of the point light (in fact 1/(r*r) is better). This ensure the value obtained is in the [0..1] relative to the current light range when writing to the cubemap.

Of note: I use CPU precalculated 1/R or 1/(r*r) passed to the constant buffer because I suppose that multiplication is faster than division on GPU as it used to be on CPU.

pixel = length(Input.WPos.xyz-LightPos[n].xyz)*LightPos[n].w;//w used to store 1/(r*r)

When using the texture the current pixel to curent pointlight distance is thus also multiplied by the reverse r*r of the current pointlight and tested against the cubemap.r channel + some bias.

float3 txDir = Input.WPos.xyz - LightPos[n].xyz;
float L= txCubeMap.Sample(sampler, txDir);
if ( L < 1 ) //cubemap filled at start with value 1: value 1 means nothing drawn, calculating shadow is useless.
  Shadow = (L + bias < length(txDir)*LightPos[n].w)?0:1; //remember w used to store 1/(r*r)

the bias value (0.002 here ) is tuned so that all my 4 point lights produce correct shadows without self shadowing of shadow casters.