Side Hcal position reconstruction

[EinarElen]

Describe the bug As Bertrand reported from his work on the v14 PN samples, the side Hcal position reconstruction isn't working right. The side hcal position reconstruction is taken directly from the Hcal geometry so the correct location to look for issues will be in building the side hcal center position map.

I've walked through all of the code leading up to this part, including the GDML and python configuration and I believe those are correct. I have also checked that the conversion from copy number to HcalID is correct on the simulation level.

Here are two sketches I made that I think is helpful to have as reference. Obviously, nothing here is to scale. A layer here corresponds to one absorber plate, two airgaps and one scintillator layer. Overview of a single section

Overview of the v14 side hcal from the front. Note the orientation of the X-axis.

Based on this sketch, I've outlined a small set of sanity checks that I'm going to check. Checked are tested and pass, checked and strikethrough are tested and fail at least once.

Top/Bottom

General features

• [x] All odd bars are oriented along the Z axis
• [x] All even bars are oriented along the X axis
• [x] All bars have have negative Y centers for the bottom section
• [x] All bars have have positive Y centers for the top section

  Features for odd bars (along Z)

• [x] Bars oriented along the Z axis all have the same Z center Bars within different modules have different Z center, e.g.
• [x] Bars oriented along the Z axis all have different X center within a given layer (offset by the width of a scintillator bar), but same as bars with the same strip number All bars within a given module currently have the same X center
• [x] Bars oriented along the Z axis all have the same Y center within a given layer, but different between different layers (offset by two times the layer thickness, taking into account the horizontal layers between)

  Features for even bars (along X)

• [x] Bars oriented along the X axis all have the same X center within a given module, but different between modules. Example bars in the same module with different X

  # Top
  Hcal(1,6,6) -> (565, 554, 565) # Both in first module, horizontal bar 
  Hcal(1,2,9) -> (715, 378, 715) # Should have same X center
  # Bottom
  Hcal(2,8,5) -> (-515, -642, 515) # Same
  Hcal(2,4,3) -> (-415, -466, 415)

  Example bars in different modules with the same X

  
  # Top
  Hcal(1,10,7) -> (615, 730, 615) # Second module, horizontal bar
  Hcal(1,2,7) -> (615, 378, 615) # First module, horizontal bar
  # Bottom
  Hcal(2,14,10) -> (-765, -906, 765) # Second module
  Hcal(2,4,10) -> (-765, -466, 765) # First module

- [x] Bars oriented along the X axis all have the same Y center within a given layer, but different between different layers (same offset as above) 
- [x] Bars oriented along the X axis all have different Z center within a layer but have the same Z center as bars with the same strip number in the other layers
- [x] ~~All bars along the X axis all have (positive) X centers for the (bottom) section~~
Fails on e.g. 

Hcal(2,8,10) -> (-765, -642, 765)

- [x] ~~All bars along the X axis all have negative X centers for the top section~~
Fails on e.g. 

Hcal(1,8,8) -> (665, 642, 665)

I think the above two issues might just be that we assume the X-axis is oriented to the right when looking from the front. But you can check either via a Geant4 geometry visualization or by looking at some hits in the HcalSD that the X-axis is oriented to the left. This is because we set the Z-direction along the beam.

This... might affect other geometries as well and possibly also the back hcal  :|

##  Left/Right (Same offsets etc, just being very explicit here) 

• [ ] All odd bars are oriented along the Z axis
• [ ] All even bars are oriented along the Y axis
• [ ] Bars oriented along the Z axis all have the same Z center
• [ ] Bars oriented along the Z axis all have different Y center within a given layer, but same as bars with the same strip number
• [ ] Bars oriented along the Z axis all have the same X center within a given layer, but different between different layers
• [ ] Bars oriented along the Y axis all have the same Y center within a given module, but different between modules.
• [ ] Bars oriented along the Y axis all have the same X center within a given layer, but different between different layers (same offset as above)
• [ ] Bars oriented along the Y axis all have different Z center within a layer but have the same Z center as bars with the same strip number in the other layers
• [ ] All bars along the Y axis all have negative (positive) Y centers for the left (right) section [Haven't checked if this holds for module 4
• [ ] All bars have have negative (positive) X centers for the left (right) section

  
  @cmantill let me know if you think I've missed anything here, its a bit complicated to keep in your head so I wouldn't be too surprised if there's something slightly off :) 

[EinarElen]

Ok, I've worked out all the issues now and tested them thoroughly. What really threw me off is that the entire Hcal geometry is offset in Y by 19.05 mm. I'm not sure why this is, but it can be corrected for relatively straight-forwardly. I'll make a PR with the patches for v14.