Reviewing the coordinate systems in play.
The first 5 are clearly defined with respect to each other, but the last is only defined internally, and I'm wondering if it is correctly defined.
In the standard orientation, the reference dowel is to the lower right, X is to the right, Y is up, and Z is toward the viewer. The R/L CCDs read in increasing Y: the larger the CCD value the larger Y will be. This is my V coordinate, and it is not in dispute here.
The Z coordinate is not measured, and will be ignored except as an orientation marker.
The X coordinate is the one that is likely to be confusing. I have claimed that on the standard transfer line the H coordinate is in the +Phi direction. I have also claimed that the standard transfer line DCOPS has the DCOPS vector (+Z) in the CMS +Z direction.
Therefore my single-line processing is correct.
Within the MAB, the DCOPS orientation will depend on whether this is the Plus or Minus side:
For the Minus side (which corresponds to a standard orientation of the DCOPS when the MAB itself is correctly oriented), X_m=-Y_D, Y_m=+Z_D, Z_m=-X_d. This corresponds to a rotation of (0,90,90) (or equivalently (90,90,180) ). However, it needs to be remembered that there is an additional 2/3 degree rotation of the DCOPS in the MAB, which is on average the same on both sides.
For the Plus side, X_m=-Y_D, Y_m=-Z_D, Z_m=+X_D. This corresponds to a rotation of (0,-90,90) (or equivalently (90,-90,0) ).
We can think of the DCOPS position as having an additional 2/3 degree rotation about Y_m. So we have for the Cocoa model on the Plus side: Ry(epsilon)*Rz(90)*Ry(-90), and for the Cocoa model on the Minus side: Ry(epsilon)*Rz(90)*Ry(90).
This gives us new rotations: Plus side=(90,-90+epsilon,0) and for the Minus side (90,90-epsilon,180) My modified version of the MAB has incorrect rotations here, I need to fix that.
In any event, for each transfer line DCOPS there are two rotations: one for the Cocoa model, and the other for my modified coordinate system. I need to spell out all of these if I am going to make the proper connections to the systems.
Update: That makes things worse.
Report for tomorrow.
Two problems: typo in the X-rotation for the Plus DCOPS, and the tilt remained. This appears to be because somehow I had the wrong sign convention for the additional rotation. This makes things slightly better than before, but not by much, and not quite as good as the original fit. There is still a problem in the model, and the obvious suspects aren't it.
The above shows the relationship of the default (untilted) H/V coordinates in the MAB system. There is nothing corresponding to CMS Z, so I will call this "nothing" Q. Without the tilt, H=Zm and V=-Xm, and for simplicity I will set Q=-Ym, which makes this look rather like the Plus side DCOPS coordinate system, in which H islike Xd and V islike Yd. Obviously the coordinate system center is different for H/V and Xd/Yd, but the directions are the same for the Plus MAB DCOPS.
This mapping does not depend on whether this is Plus or Minus.
CMS position = X_MAB + R_MAB ( X_DCOPS + R_DCOPS * (X_DCOPS_CENTER) + R_Special*(X_HVQ))
H and V are defined from the center of the DCOPS CCDs, not from the dowel or virtual dowel. The R_Special will be the same as R_DCOPS for the Plus side MAB DCOPS, but will be different for the Minus side ones.
Something similar pertains to the Endcap DCOPS. In this case we have a more complex prefix:
CMS position = X_DISK + R_DISK ( X_SLM + R_SLM ( X_TRANSFER + R_TRANSFER (X_DCOPS + R_DCOPS (X_DCOPS_CENTER) + R_Special * X_HVQ)))
In this case, since we are using a standard aperture for all the Endcap DCOPS (even though they aren't all the same size) we use a single X_DCOPS_CENTER for all of them. The R_Special will only take one of 4 different types (perhaps only 2), and I don't have reliable estimates for tilts.
The orientation of the Endcap DCOPS is defined as positive if the local Z-vector is in the +Z CMS direction, and negative if the local Z-vector is in the -Z CMS direction. The HVQ system is thus more like the "negative" orientation DCOPS, and the R_Special will be the same as the R_DCOPS for those cases. For the "positive" orientation DCOPS we need a different rotation.
From Oleg's table the negative orientation DCOPS are
ME+4/2 ME+3/2 ME+2/2 ME-2/2 ME-3/2 ME-4/3 ME+1/3 ME-1/3 ME+4/4 ME+3/4 ME+2/4 ME+1/4 ME-1/4 ME-2/4 ME-3/4 ME-4/4 ME+3/5 ME-3/5 ME+4/6 ME+3/6 ME+2/6 ME-2/6 ME-3/6 ME-4/6
The postive orientation DCOPS (requiring new rotations) are
ME+4/1 ME+3/1 ME+2/1 ME+1/1 ME-1/1 ME-2/1 ME-3/1 ME-4/1 ME+1/2 ME-1/2 ME+4/3 ME+3/3 ME+2/3 ME-2/3 ME-3/3 ME-4/3 ME+4/5 ME+2/5 ME+1/5 ME-1/5 ME-2/5 ME-4/5 ME+1/6 ME-1/6
The results seems simple enough: there are 4 kinds of R_Special, summarized in rotlist.endcap
grep ME rotlist.endcap | awk '{split($1,a,"=");print "R_Special_"a[1]"=rotationD("$2")";}' | sed 's/_R_/_/' > specialDCOPSrotations.gp
specialDCOPSrotations.gp should be the Endcap rotations required to map the HVQ system into the Endcap transfer plate system.
Similarly we have rotlist.mab for the MAB rotations. Note that all the Special rotations have the form of the the Plus rotation, including individual tilts for each DCOPS.
grep MA rotlist.mab | awk '{split($1,a,"=");print "R_Special_"a[1]"=rotationD("$2")";}' | sed 's/_R_/_/' > specialDCOPSrotationsMAB.gp
specialDCOPSrotationsMAB.gp should be the MAB rotations required to map the HVQ system into the MAB coordinate system. I will always set Q=0.
Modified 02-September-2010 at 13:53
http://hep.physics.wisc.edu/~jnb/cms/02Sep2010
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