Omnidirectional shadow mapping with depth cubemap

Question

I\'m working with omnidirectional point lights. I already implemented shadow mapping using a cubemap texture as color attachement of 6 framebuffers, and encoding the light-t

Answer 1

I would like to add more details regarding the derivation.

Let V be the light-to-fragment direction vector.

As Benlitz already said, the Z value in the respective cube side frustum/"eye space" can be calculated by taking the max of the absolute values of V's components.

Z = max(abs(V.x),abs(V.y),abs(V.z))

Then, to be precise, we should negate Z because in OpenGL, the negative Z-axis points into the screen/view frustum.

Now we want to get the depth buffer "compatible" value of that -Z.

Looking at the OpenGL perspective matrix...

http://www.songho.ca/opengl/files/gl_projectionmatrix_eq16.png

http://i.stack.imgur.com/mN7ke.png (backup link)

...we see that, for any homogeneous vector multiplied with that matrix, the resulting z value is completely independent of the vector's x and y components.

So we can simply multiply this matrix with the homogeneous vector (0,0,-Z,1) and we get the vector (components):

x = 0
y = 0
z = (-Z * -(f+n) / (f-n)) + (-2*f*n / (f-n))
w = Z

Then we need to do the perspective divide, so we divide z by w (Z) which gives us:

z' = (f+n) / (f-n) - 2*f*n / (Z* (f-n))

This z' is in OpenGL's normalized device coordinate (NDC) range [-1,1] and needs to be transformed into a depth buffer compatible range of [0,1]:

z_depth_buffer_compatible = (z' + 1.0) * 0.5

Further notes:

• It might make sense to upload the results of (f+n), (f-n) and (f*n) as shader uniforms to save computation.

• V needs to be in world space since the shadow cube map is normally axis aligned in world space thus the "max(abs(V.x),abs(V.y),abs(V.z))"-part only works if V is a world space direction vector.