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Subject: Re: Find the correspondent coordinates of a unit sphere in a sphere of radius X
Date: Sun, 2 Dec 2012 18:14:08 +0000 (UTC)
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"Javier " <javsanzperez@gmail.com> wrote in message <k9fj58$j44$1@newscl01ah.mathworks.com>...
> .....  find the correspondent coordinates of a unit sphere in a sphere of radius X.  ......
- - - - - - - - - -
  Let P1 = (x1;y1;z1] be the coordinates of some point on a sphere of radius R1 with center located at C1 = [u1;v1;w1] and let P2 = [x2;y2;z2] be the coordinates of the corresponding point on a sphere of radius R2 with center at C2 = [u2;v2;w2].  Then P2 can be expressed in terms of P1 by the vector equation:

 P2 = C2 + (R2/R1)*(P1-C1);

  This amounts to a translation from center C1 to center C2 followed by an expansion by the ratio R2/R1, and, as you see, it is a linear expression.

Roger Stafford