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November 2nd, 2010, 12:03 PM   #1
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Detector geometry (affine space)

Hi All,

I have some problem with my calculations of the area X-ray detector geometry. Below I present my problem in details.

Assume we have two Cartesian coordinate systems (bases) in the 3D space, and . They are anchored in points and , respectively. Base is constructed from in such a way: (1) basis vectors are rotated by , and axes (by a small angles, these are detector tilt angles); (2) the coordinate system is moved by distance along axis; (3) it is moved along , and axes by , and distances, respectively (these are mechanical offsets which I'd like to consider).

Now, I have a unit vector , anchored at point . I would like to calculate the point of intersection of elongation of this vector (i.e. ) with the plane (defined by vectors and ). I was trying to calculate this but I'm completely stuck...

Any help is greatly acknowledged.

Regards,

Radek
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