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for a homework assignment I am supposed to compute the intersection between two lines in 3D. One of them is defined by the camera center, a direction vector and rotation matrix. Unfortunately, I don't understand how I can get the Plücker matrix line representation from that.

Plücker coordinates are defined as $L = (q, q')$ where $q$ is the direction vector of the line and $q'$ the plane normal (of the plane defined by the origin and the line) as far as I know.

But I have no idea how this would work with the information I have. Could anyone please give me a hint?

chibi03
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  • Convert the Cartesian coordinates of the camera center and direction vector into homogeneous coordinates. – amd May 25 '19 at 17:21
  • apologies, I still don't get it. What do I do with these then? Can I get another point that lies on the line with these somehow? – chibi03 May 25 '19 at 18:01
  • Why do you need a rotation matrix? – Somos May 25 '19 at 18:38
  • The Plücker matrix of the line through points $\mathbf p$ and $\mathbf q$ is $\mathbf p\mathbf q^T-\mathbf q\mathbf p^T$. The camera center and direction vector are your two points. Plücker coordinates, while related to the matrix, are something else. – amd May 25 '19 at 21:47

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