how do I get a projection matrix I can use for a pointlight shadow map?

Question

I'm currently working on a project that uses shadowtextures to render shadows.
It was pretty easy for spotlights, since only 1 texture in the direction of the spotlight is needed, but its a little more difficult since it needs either 6 textures in all directions or 1 texture that somehow renders all the obects around the pointlight.
And thats where my problem is. How can I generate a Projection matrix that somehow renders all the object in a 360 angle around the pointlight?
Basicly how do create a fisheye (or any other 360 degree camera) vertex shader?

Answer 1

How can I generate a Projection matrix that somehow renders all the object in a 360 angle around the pointlight?

You can't. A 4x4 projection matrix in homogenous space cannot represent any operation which would result in bending the edges of polygons. A straight line stays a straight line.

Basicly how do create a fisheye (or any other 360 degree camera) vertex shader?

You can't do that either, at least not in the general case. And this is not a limit of the projection matrix in use, but a general limit of the rasterizer. You could of course put the formula for fisheye distortion into the vertex shader. But the rasterizer will still rasterize each triangle with straight edges, you just distort the position of the corner points of each triangle. This means that it will only be correct for tiny triangles covering a single pixel. For larger triangles, you completely screw up the image. If you have stuff like T-joints, this even results in holes or overlaps in objects which actually should be perfectly closed.

It was pretty easy for spotlights, since only 1 texture in the direction of the spotlight is needed, but its a little more difficult since it needs either 6 textures in all directions or 1 texture that somehow renders all the obects around the pointlight.

The correct solution for this would be using a single cube map texture, with provides 6 faces. In a perfect cube, each face can then be rendered by a standard symmetric perspective projection with a field of view of 90 degrees both horizontally and vertically.

In modern OpenGL, you can use layered rendering. In that case, you attach each of the 6 faces of the cube map as a single layer to an FBO, and you can use the geometry shader to amplify your geomerty 6 times, and transform it according to the 6 different projection matrices, so that you still only need one render pass for the complete shadow map.

There are some other vendor-specific extensions which might be used to further optimize the cube map rendering, like Nvidia's NV_viewport_swizzle (available on Maxwell and newer GPUs), but I only mention this for completness.