将球体投影到立方体上

I'm currently working on building a game which is on a planet, the way in which I'm planning to store the data is in 6 2dimensional arrays, which are heightmaps around the sphere (on the faces of a cube). The problem I have is this, given a normalised vector which points outwards from the centre of the sphere how can I determine these two things:I'm currently working on building a game which