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This figure shows one such mapping.  It is the polar coordinate of the ACD, as seen from a point 600mm below the Z=0 plane of the LAT.

   Image Added
 
Given x,y,z the transformations to the new coordinates (u,v) are:

    double dist2 = x*x + y*y;
    double dist = sqrt(dist2);
    double zVal = z + 600.;
    double rad = atan2( dist , zVal );
    double u = rad * ( x / dist );
    double v = rad * ( y / dist );
 

 Then we divide the u,v plane into 20 segments in each direction, making 400 possible bins.

At the start of the reconstruction job we pre-compute the look-up table.   To build in tolerance we increase the size of all the detector elements by some amount (say 200mm), then we scan across the detector element in 10x10 steps (100 points per detector) for each point we get the (u,v) bin the point falls in a add this to the overall map.  Technically speaking the map is

 std std::map< AcdRecon::AcdUVBin, std::list< idents::AcdId > > >
 

 Then for each track in each event we

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