Matrix question

  • Thread starter orochimaru
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orochimaru

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Hi,
i need enlightenment on this question of mine.

Suppose i have two lines, L and M.
L and M intersect at point X.
Then is X a cross product of L and M?

I read this from a pdf on Multiple View Geometry.
Here the link http://www.syseng.anu.edu.au/~hartley/Papers/CVPR99-tutorial/tut_4up.pdf
the eqn is on pg 8 top right corner slide.

Thanks in advance!
 

Answers and Replies

TD
Homework Helper
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Yes, that is correct.

For example, take the lines [itex]x + y + 1 = 0[/itex] and [itex]-x + 2y = 0[/itex] with vector representations (according to your pdf file) [itex]\left( {1,1,1} \right)[/itex] and [itex]\left( {-1,2,0} \right)[/itex].

The cross product is [itex]\left( {1,1,1} \right) \times \left( { - 1,2,0} \right) = \left( {2,1, - 3} \right)[/itex]. Dividing by -3 to get the z-component to equal 1 gives the cartesian intersection point of [itex]\left( { - \frac{2}{3}, - \frac{1}{3}} \right)[/itex]
 

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