OpenGL Custom Projections?

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The only 2 projects I know of that are built into OpenGL are Orthographic and Perspective. I've been using these for a while now but am wondering if it's possible to have other projection types...like stereographic. I've searched Google for code for this but have come up empty-handed. My current project is to be purely based on this projection type. I've realized that other programs written with OpenGL, like stellarium, seem to be able to do this. However, I'm not about to look through 1M+ lines of code just to find a few hundred that I need (not to mention that stellarium has SO few comments). If possible, I'd like to see some example code and a brief explanation (unless the code is self-explanatory). Thanks.

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The projection matrix used in OpenGL is supposed to map all 3d points within some volume onto a 2d plane.

Stereographic projection seems to map only points located on a sphere (except for one, the projection point) onto a 2d plane.

So I think you'd have to something on your own to achieve the effect you want (I'm not sure what that is, exactly, so I can't offer any more help).

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Yes, that's what I'm trying to figure out how to do. I'm trying to convert everything 3D and draw it onto a sphere which then needs to be converted to 2D with a stereographic projection. I'm sure this is possible (to some extent) as, like I said, stellarium uses it (and the objects appear remarkably 3D as if drawn using Perspective).

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I'm not entirely sure if this is what you want, but here goes.

Why don't you render your scene 6 times in 6 directions: up, down, left, right, forward, backward. Just like if you were making a cubemap.

Then, you just need a mapping from the 6-sided cube to a sphere. After that, you can go from the sphere to 2d plane via the Stereographic projection like you wanted.

So in the end, you'd have to render a big quad that covers the entire screen. For each pixel, you want to go from the 2d position -> position on a sphere (inverse Stereographic projection), and then from a position on the sphere to a position on the cube. Then, sample the texture of the side of the cube that you hit.

Essentially, you'd be doing something very similar to Sperical/Cube Environment Mapping, except done in reverse.

I have no idea if that's what you're looking for, or if this helps at all (you'd have to know shaders to implement the above), but good luck.

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I haven't a clue about how to do this but I will take a look at some of those tutorials. (I've never rendered anything successfully on the inside of a polyhedron or any other solid)

Also, if anyone else has a solution, please post. Stereographic Projections on Wikipedia: http://en.wikipedia.org/wiki/Stereographic_projection (there are formulas but no matrices).

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