Cubic to equirectangular projection algorithm

Question

I have a cube map texture which defines a surrounding, however I need to pass it to a program which only works with latitude/longitude maps. I am really at lost here on how to d

Answer 1

A general procedure for projecting raster images like this is:

for each pixel of the destination image:
    calculate the corresponding unit vector in 3-dimensional space
    calculate the x,y coordinate for that vector in the source image
    sample the source image at that coordinate and assign the value to the destination pixel

The last step is simply interpolation. We will focus on the other two steps.

The unit vector for a given latitude and longitude is (+z towards the north pole, +x towards the prime meridian):

x = cos(lat)*cos(lon)
y = cos(lat)*sin(lon)
z = sin(lat)

Assume the cube is +/- 1 unit around the origin (i.e. 2x2x2 overall size). Once we have the unit vector, we can find the face of the cube it's on by looking at the element with the largest absolute value. For example, if our unit vector was <0.2099, -0.7289, 0.6516>, then the y element has the largest absolute value. It's negative, so the point will be found on the -y face of the cube. Normalize the other two coordinates by dividing by the y magnitude to get the location within that face. So, the point will be at x=0.2879, z=0.8939 on the -y face.