Calculating UV coordinates for sampling texture atlas

Question

I have an 8192x8192 texture atlas that contains 1024x1024 shadow maps aligned side by side. I'm trying to calculate the uv coordinates so that I can sample each shadow map appropriately based on the 'shadowIndex' of my light. With a single non-atlas shadowmap I can easily calculate the uv coordinates like this:

tc.x = lightViewPosition.x / lightViewPosition.w / 2.0f + 0.5f;
tc.y = -lightViewPosition.y / lightViewPosition.w / 2.0f + 0.5f;

shadowFactor += shadowMap.SampleCmpLevelZero(SampleComp, tc, lightDepthValue);

How can I replicate the same thing while also factoring in an offset for sampling the correct shadow map from the atlas? I tried this:

tc.x = lightViewPosition.x / lightViewPosition.w / 2.0f + 0.5f;
tc.y = -lightViewPosition.y / lightViewPosition.w / 2.0f + 0.5f;

float tileSize = 1024.0f / 8.0f;
float tileOffset = tileSize * lights[i].shadowIndex;

tc += frac((tc - tileOffset) / tileSize) * tileSize + tileOffset;

But this does not work correctly. Additionally I have to consider that the y (V) coordinate should not be affected while the shadow index isn't a multiple of 8 because there are 8 shadow maps per row. Any ideas? Thanks.

Answer 1

Assuming normalized texture coordinates and a grid of 8x8 (which is 64 tiles not 16 like I said in the comments) then tileOffset will need to be a vec2 for the x and y offsets.

Also, assuming texture coordinates tc are mapped to a single texture map (0,1).

Then the new texture coordinates for tile 0,0 are tc = (tc*vec2(1024,1024))/vec2(8192,8192); For tile 1 the texture coordinates would added 1024/8192 to the tc.x, tile two would add 2048/8192 to tc.x and so forth up to tile 8.

tc.y doesn't change till tile 8 which then gets 1024/8192 added to it until tile 16 and so forth.

So the tile specific texture coords would be

tc = (tc*vec2(1024,1024))/vec2(8192,8192);
tc.x += ((lights[i].shadowIndex % 8) * 1024)/8192.0;
tc.y += ((lights[i].shadowIndex / 8) * 1024)/8192.0;

Where the %8 and /8 are indicating integer modulus and division. This is just psudo code and I was using the upper left corner as 0,0 but the idea is the same for other origins.

Edit: The code is converting normalized coordinates to unnormalized coordinates for a texture map size of 1024x1024. Then converting that to normalized coordinates for a texture maps size of 8192x8192.

Then it computes the normalized offsets for x and y and adds them to get the grid specific location.