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Suppose I have a sphere. Inside the sphere I have an inscribed cube. What I am interested in is finding out what is the latitude and longitude (or coordinates) of a point on the sphere which will be projected on a cube's face given the coodinate of a point on one of the cube's faces.

Does anyone have any equations for this?

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    Is this the same as [this earlier question](http://math.stackexchange.com/questions/86484/equirectangular-to-cube-faces-projection)?2011-11-28

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Here I assume, since it is not specified in the question, that the projection is taken along the radius ray.

Suppose $(x,y,z)$ denote coordinate of a point on a cube with unit-edge length and position so that its centroid is exactly at the origin. The radius of the circumscribed sphere is $\frac{\sqrt{3}}{2} $. The coodinates of point's projection onto the sphere are: $ (x^\prime,y^\prime,z^\prime) = (x,y,z) \frac{1}{2} \sqrt{\frac{3}{x^2+y^2+z^2}} $ You can now work on mapping these into spherical coordinates as needed.

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    @Ryan Coordinates of cube's vertexes are $\left( \pm\frac{1}{2}, \pm\frac{1}{2}, \pm\frac{1}{2} \right)$. The square of the distance from any of it to the origin is $\frac{3}{4}$, so yes, you are correct! My bad, sorry.2011-11-29