Shadow-Map approximation with Parallax-Mapping

Maybe you could draw a picture?
You talk about directional lights having positions instead of directions... Is the fact that the triangle is equilateral relevant? Why is one light's shadow map being derived from 3 other shadow maps? If the triangle has a texture, the texture is located on the triangle, right? Why does the size of the triangle in "units" change anything? I don't get it.

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Original post by HodgmanYou talk about directional lights having positions instead of directions...

I built a huge sphere surrounding the scene with many directional lights to simulate ambient light while still being able to incorporate self occlusions.

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Is the fact that the triangle is equilateral relevant?

No, just made this constraint to keep it as easy and understandable as possible.

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Why is one light's shadow map being derived from 3 other shadow maps?

This was also determined by me. You could probably go with 2 or more than 3 but you'll probably get the best results in terms of cost/performance ratio with 3.

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If the triangle has a texture, the texture is located on the triangle, right? Why does the size of the triangle in "units" change anything? I don't get it.

Hopefully my answer to your first question did clarify this. The surrounding sphere is not a rigid object. It just defines how the directional lights are arranged to simulate ambient light as good as possible.
Now in order to compute shadows for a scene you'd have to calculate shadow maps for every single directional light which is pretty expensive. But because you know that the lights are pretty close together it might be a good idea to approximate some shadow maps by using the shadow maps of some adjancent lights.
This should apparently work with parallax mapping but I'm not sure how.

Ok lets simplify this:

Parallax-Mapping is able to generate a new view from a texture + corresponding height map. Now lets say I generate a shadow map of a scene from viewpoint A and want to approximate a shadow map for viewpoint B whose relative position/orientation to A is known. How does that work?

The problem is that I don't have a texture anymore but solely a shadow map. Additionally, to generate parallax I have to raytrace the texture but since the shadow map doesn't lie on a solid object it doesn't have a location in space and therefore can't be raytraced.

Does this make any sense now?

Lets even simplify this more ;)

We create a shadow map from the view of one directional light (parallel-projection!). Now we have another directional light whose distance and orientation relative to the first directional light are known.
How can we approximate a view for the 2nd light from the first one?