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Topic: Find the correspondent coordinates of a unit sphere in a sphere of radius X
Replies: 2   Last Post: Dec 3, 2012 8:05 AM

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Javier

Posts: 61
Registered: 4/26/11
Re: Find the correspondent coordinates of a unit sphere in a sphere of radius X
Posted: Dec 3, 2012 8:05 AM
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"Roger Stafford" wrote in message <k9g5pg$g8d$1@newscl01ah.mathworks.com>...
> "Javier " <javsanzperez@gmail.com> wrote in message <k9fj58$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


Thanks very much, Roger!



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