How do I convert a cube map to an equirectangular projection?

Question

I have a cube map texture showing a surrounding area, which I want to pass to a program that only works with latitude/longitude maps.

How can I do this?

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In other words, I need to turn this:

…into this (I think it's additionally rotated -90° over the x axis):

Answer 1

With rect_coordinate ranging from -1 to 1 and assuming sin/cos functions take radian as inputs, for each pixel in the rectangular texture do:

color CubeToRectangle(vec2 rect_coordinate)
{
    vec3 cube_map_coordinate;

    cube_map_coordinate.x = cos(rect_coordinate.x * PI * 2) * cos(rect_coordinate.y * PI);
    cube_map_coordinate.y = sin(rect_coordinate.y * PI);
    cube_map_coordinate.z = sin(rect_coordinate.x * PI * 2) * cos(rect_coordinate.y * PI);

    return CubeMapTextureRead(cube_map_coordinate);
}