Rendering a point light using 6 spot lights?

Question

I'm trying to render 6 spot lights to create a point light for a shadow mapping algorithm.

I'm not sure if I'm doing this right, I've more or less followed the instructions here when setting up my view and projection matrices but the end result looks like this:

White areas are parts which are covered by one of the 6 shadow maps, the darker areas are ones which aren't covered by the shadowmaps. Obviously I don't have a problem with the teapots and boxes having their shadows projected onto the scene, however as you can see the 6 shadow maps have blindspots. Is this how a cubed shadow map is supposed to look? It doesn't look like a shadowmap of a point light source...

Answer 1

What you're seeing here are a circle and two hyperbolas -- conic sections -- exactly the result you might expect if you took a double ended cone and intersected it with a plane.

This math may seem removed from the situation but it explains your problem. A spotlight creates a cone of light, and you can't entirely fill a solid space with a bunch of cones coming from the same point. (I'd suggest rolling up a bunch of pieces of paper and taping them together at the points to try it out.)

However, as you get far from the origin of your simulated-point-source, the cones converge to their assymptotes, and there is an infinitesimally-narrow gap in the light.

One option to solve this is to change the focus of the cones so that they overlap slightly -- this will create areas that are overexposed, but the overexposure will only become obvious as you get farther away. So long as all of your objects are near the point light source, this might not be much of an issue.

Another option is to move the focus of all of the lights much closer to their sources. This way, they'd converge to their assymptotes more quickly.

Answer 2

Actually you can adjust your six spots to have cones that perfectly fill each face of your cubemap. You can achieve this by setting each cone's aperture to create a circumscribed circle around each cubemap face. In this case you don't have to worry about overlapping, since the would be overlapping parts are out of the faces' area.

In other terms: adjust the lights' projection matrix' FOV, so it won't the view frustum that includes the light cone, but the cone will include the view frustum.

The a whole implementation see this paper.