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November 2nd, 2010, 12:03 PM  #1 
Newbie Joined: Nov 2010 Posts: 8 Thanks: 0  Detector geometry (affine space)
Hi All, I have some problem with my calculations of the area Xray 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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affine, detector, geometry, space 
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