I'm not very good with transforming things from one space to another, so I'll try to go through this one by one and see if I understand it.

// Reconstruct view-space position from the depth buffer
float pixelDepth = DepthMap.Sample(DepthMapSampler, input.TexCoord).r;
float4 position = float4(pixelDepth * input.FrustumCornerVS, 1.0f);

The comment from the sample says that position is going to be in view-space, which fits the assumption your equation makes. I've never seen this kind of position reconstruction before and don't really understand it, so I can only assume it's doing what it says.

The next part is:

float4x4 inverseLVP = mul(InverseView, lightViewProjection);
float4 positionLight = mul(position, inverseLVP);

InverseView here is the inverse of the player's camera's view matrix. lightViewProjection is the View * Projection matrix for the cascade camera this pixel is in. Broken down, mul(position, InverseView) matches your step 1. inverse(L) should be the view matrix for the cascade camera and L_proj the projection matrix. So in mine it's combined into 1 matrix. So I think it is going through the right transforms, right?

I'm not very good with transforming things from one space to another, so I'll try to go through this one by one and see if I understand it.

// Reconstruct view-space position from the depth buffer
float pixelDepth = DepthMap.Sample(DepthMapSampler, input.TexCoord).r;
float4 position = float4(pixelDepth * input.FrustumCornerVS, 1.0f);

The comment from the sample says that position is going to be in view-space, which fits the assumption your equation makes. I've never seen this kind of position reconstruction before and don't really understand it, so I can only assume its doing what it says.

The next part is:

float4x4 inverseLVP = mul(InverseView, lightViewProjection);
float4 positionLight = mul(position, inverseLVP);

InverseView here is the inverse of the player's camera's view matrix. lightViewProjection is the View * Projection matrix for the cascade camera this pixel is in. Broken down, mul(position, InverseView) matches your step 1. inverse(L) should be the view matrix for the cascade camera and L_proj the projection matrix. So in mine it's combined into 1 matrix. So I think it is going through the right transforms, right?

I'm not very good with transforming things from one space to another, so I'll try to go through this one by one and see if I understand it.

// Reconstruct view-space position from the depth buffer
float pixelDepth = DepthMap.Sample(DepthMapSampler, input.TexCoord).r;
float4 position = float4(pixelDepth * input.FrustumCornerVS, 1.0f);

The comment from the sample says that position is going to be in view-space, which fits the assumption you're equation makes. I've never seen this kind of position reconstruction before and don't really understand it, so I can only assume its doing what it says.

The next part is:

float4x4 inverseLVP = mul(InverseView, lightViewProjection);
float4 positionLight = mul(position, inverseLVP);

InverseView here is the inverse of the player's camera's view matrix. lightViewProjection is the View * Projection matrix for the cascade camera this pixel is in. Broken down, mul(position, InverseView) matches your step 1. inverse(L) should be the view matrix for the cascade camera and L_proj the projection matrix. So in mine it's combined into 1 matrix. So I think it is going through the right transforms, right?