Is a dynamic enviroment map using pincushion curvilinear perspective projection possible?

Question

I'm wondering if it is possible to generate a dynamic spherical environment map using a single frame render using a pincushion curvilinear perspective projection matrix (phew, that's a mouthful)?

I've been researching this for a few days now and the closest thing I can find is a curvilinear perspective but it isn't a commonly used projection matrix so there isn't any help I was easily able to find and I still don't know if it supports a full circle FOV.

Why?

The standard perspective matrix but it begins to look very strange and distorted above 180 degrees vertical FOV and completely fails to render when approaching 360 degrees. So instead most games render the scene six times using 90 degree FOV facing the faces of a cube.

Rendering the scene 6 times seems like a waste if it might be possible to simply imagine a camera that has a 360 degree view across both axis and then render that to a spherical environment map.

Answer 1

In practice, even when a scene is built to minimise problems, a 360-degree-FOV camera tends to introduce so much distortion in some directions that its results are useless for most purposes.

If you want to avoid the expense of rendering a full texture cube, you can get a similar effect by using dual paraboloid environment maps, in which you render two parabolic views of the scene, and then use those two resulting images as your environment map, instead of using a texture cube's six maps.

Answer 2

The short answer is: yes, it is possible, but since the projection you desire is nonlinear, you must do one of two things:

• Subdivide the geometry finely and implement the projection math in the vertex shader (or domain shader if using hardware tessellation), or
• Render a standard environment map (e.g. cubemap) first and then resample it to the desired projection using a post-processing pass.

For more details you can see my answer to this related question, where I've talked about this at greater length.

The takeaway, though, is that rendering with a nonlinear projection generally requires you to do some sort of extra work and isn't terribly likely to be an optimization over simply rendering a cubemap, despite the fact that you then have to draw the scene six times (or, perhaps better, use a geometry shader to replicate primitives to all cube faces).