Re: [ATM] Another Math Question

["Carlos Davila" <comunerito@gmail.com>]

On Fri, May 16, 2008 at 10:49 PM, Richard F.L.R. Snashall <rflrs@rcn.com> wrote:
> I'm trying to solve a problem in R^3.  I have a point P0 and
> a [unit] direction P0'.  I also have another point P1.  I want
> to find the minimal distance of P1 from the ray path given by
> P0 and P0'.

Richard,

I am not sure what you mean by "relative position not in the direction
of propagation". If what you seek is the minimum distance from P1 to
any point along the line though the origin and P0, you must first find
the orthogonal projection of P1 onto P0:

<P1, P0>
------------- * P0 = P1_hat
<P0, P0>

where <a, b> is the dot product between a and b. The minimum distance
you seek is:

<P1 - P1_hat, P1 - P1_hat>^{1/2}

See http://en.wikipedia.org/wiki/Orthogonal_projection for a somewhat
more general treatment of projections.

Your formula would be correct if you replaced R1 with P1.

With regards,
Carlos
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