Q: How to generate the shadow map for each of split parts?

A: The view frustum is split into several parts {V_i}, by using the clip planes parallel to the near plane at split positions {C_i}. Then we compute the intersected space between V_i and the light's frustum W. The "intersection" operations result in a sequence of sub-spaces {W_i}. Like standard shadow mapping, we render a shadow map T_i for each V_i. But here we should notice that the current light's view space is W_i (not W!) when we render T_i. More importantly, the pixel also needs to be transformed into the corresponding sub-space rather than W during shadow determinations. Different shadow map reparameterizations can be applied in different depth layers when generating shadow maps.

Due to the bias of the floating-point number on hardware, we'd better introduce a very small intersection between adjacent split parts. In our implementation, a trivial bias was used for each split position C_i to remove the floating-point errors.