### Theory NO. 6 : A point projection matrix to a line (3D)

29Apr09

I was trying to get a matrix for a projection of any point to a line given by the following equotations:

$x=at$
$y=bt$
$z=ct$

After some time of research I’ve ended with the following result:
Let $r=a^2+b^2+c^2$ then
$M= \left ( \begin{matrix} a^2/r & ba/r & ca/r \\ ab/r & b^2/r & cb/r \\ ac/r & bc/r & c^2/r \end{matrix} \right )$

Of course the result isn’t new at all, it was just a big efford for me to do that at midnight – so I guess it may be worth saving it here.

#### One Response to “Theory NO. 6 : A point projection matrix to a line (3D)”

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