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I have 2 points in space, defined by their spherical coordinates.

I'd like to know the spherical coordinates of the second point in a reference system centered on the first point (I know the unit vector defining x,y, and z in the new reference system, obviously).

Is there a standard way to calclate the new coordinates, without having to convert to/from cartesian first?

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I tried this a few weeks ago using only geometry and gave up because it was taking too long. I think you have to use cartesians and then change it back to spherical polars (at least, I couldn't see any other way). I got 3 horrible equations, one for each coordinate. By the end of it all, I forgot what I had set out to do in the first place... so I am interested... do you know why you are doing this? –  Adam Rubinson May 9 '12 at 18:17
    
I'm currently working on augmented reality, and our current approach involves a lot of approximations, and conversions (and loss of precision). If we could get the points in the viewer's coordinate system, calculations would be much easier / faster. –  G B May 10 '12 at 7:00
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