Implements general rotation order

[pranphy]

A new tag <orotation> is created that can be used in GDML files for ordered rotation.

<orotation unit="degree" x="45" y="25" z="90" order="zxy"/>

this would allow the rotation 𝑅𝑧(90) → 𝑅𝑥(45) → 𝑅𝑦(25). The value of order parameter can be
any of the six permutations of string “xyz”.

Example:

▶ Yellow: Unrotated
▶ Green: 𝑅𝑥(90) → 𝑅𝑦(45) → 𝑅𝑧(0)
▶ Orange: 𝑅𝑦(45) → 𝑅𝑥(90) → 𝑅𝑧(0)
▶ there is a translation between them

Ref: DocDB:1199

[wdconinc]

FYI, this will not be valid GDML anymore. It will make schema validation always fail (unless you update the DTD in a derived schema and maintain that too). No other tools that interpret GDML (such are ROOT, FreeCAD) will be able to be used again. Be sure you know what you're doing when you merge this.

[pranphy]

@wdconinc Thank you for your comment. Does remoll/Geant4 parser do the schema validation by default? If we only ever use the gdml for remoll, only within remoll then it should be ok right?
Also do you have a suggestion on how to implement the altered rotation order without breaking standard gdml schema?

[wdconinc]

Also do you have a suggestion on how to implement the altered rotation order without breaking standard gdml schema?

Any rotation can be written as a rotation around three orthogonal axes, so there is a conversion, but it's probably not what you want to implement:

// from https://github.com/JeffersonLab/remoll/pull/611/files#diff-09868a28f9dae1133da8e941378ccc7725148e0979ae16308a56bcb8e324e14bR143
rxz = ROOT::Math::RotationZ(51.41960449999*TMath::DegToRad())*ROOT::Math::RotationX(3.00110158279097*TMath::DegToRad())
rzyx = ROOT::Math::RotationZYX(rxz)
cout << "x=" << rzyx.Psi() << " y=" << rzyx.Theta() << " z=" << rzyx.Phi() << std::endl;
ROOT::Math::Cartesian3D<double> v(1,1,1)
vp = rxz * v
vp2 = rzyx * v
cout << "x=" << vp.X() << " " << vp2.X() << " y=" <<  vp.Y() << " " << vp2.Y() << " z=" <<  vp.Z() << " " << vp2.Z() << std::endl;

produces:

x=0.0326825 y=0.0409392 z=0.896772
x=-0.116122 -0.116122 y=1.37184 1.37184 z=1.05098 1.05098

Easier may be to put the x rotations in e.g. geometry/detector/ThinQuartz/DetectorArray/FFSeg1_R5-FF-Quartz_L.gdml, and only do the z rotation in geometry/detector/ThinQuartz/DetectorArray/DetectorArray.gdml. That keeps the geometry modular.

[cipriangal]

The layout of the quartz tiles using this new o-rotation

[cipriangal]

@pranphy : We should discuss Wouter's suggestion at the simulation meeting today.