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I have a set of points $P$ on the surface of a sphere of radius $R$. I wish to change the radius of the sphere to $R_2 = c*R_1$, where $c$ is some positive real number. Using Cartesian coordinates, how do I map the set of points $P$ to the surface of the new sphere such that the distance between the points remains proportionally the same?

Please assume that we know the point $p_s$ at the center of the sphere. We can set $p_s = (0,0,0)$.

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up vote 0 down vote accepted

$(x,y,z) \mapsto (cx,cy,cz)$ (assuming the spheres are both centered at the origin)

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Thanks I didn't know if this was a bias-free way of doing things. – user65106 Mar 5 '13 at 10:27
Not sure what you mean by "bias", but this mapping will keep distances proportional. – bubba Mar 5 '13 at 11:00

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