Hall A Analyzer

Made the geometry of the VDC classes consistent. There are two main coordinate systems:

1. VDC coordinates: The origin is the center of the lower VDC chamber, z points vertically up, x is horizontal along the long VDC side in the dispersive direction (pointing away from the target)
2. Track coordinates (also called TRANSPORT coordinates, although that's misleading): The origin is the same as that of the VDC coordinate system. z points along the direction of the central ray, y is the same as the VDC system's y, and x forms a right-handed coordinate system with z and y. The direction of the central ray is the VDC z-axis tilted by a little over 45 toward the VDC x-axis. This angle is the (negative of the) "VDC angle", specified as the T000 focal plane matrix element in the database. Yes, I know, a complicated mess.

VDC track calculations are first done in the VDC systems. Track system coordinates are then calculated in THaVDC::CalcFocalPlaneCoords. All detector fOrigin and axes (fXax etc.) are given relative to the track system. So the VDC axes are tilted by -45.1 or so degrees, while detectors usually aren't tilted (although they can be).

The center point of each VDC plane is now in a new TVector3 member variable THaVDCPlane::fCenter, which is expressed in VDC coordinates. THaVDCPlane::fOrigin is that same point, but in track coordinates. The x and y components of fCenter are now calculated automatically from the wire start positions, except if non-zero values are given for x and/or y in the database, they override the calculated positions. In practice, y is always zero by definition, and so is x of the lower chamber.

To check if a point lies within a detector's active area, use IsInactiveArea(x,y), where x and y must be in local detector coordinates, except for THaVDCPlane, where x and y are in VDC coordinates (i.e. not the THaVDCPlane local system), i.e. relative to fOrigin = (0,0,0).

THaVDCChamber::MatchUVClusters() now correctly checks if a cluster is inside the active VDC area. The VDC plane "size" is set to approximate, conservative values for the HRS VDCs in THaVDCPlane::ReadGeometry so that this cut already works to some extent with old databases. To adjust the cut, specify "size" explicitly in the database.

Most of this is implemented with commit 7751e5f.