class HEDTransform: public TObject

 returns the lower phi bound of the sector
 in LAB [Deg].

 offset xyz + rotation in deg

 offset xyz + rotation in deg

 get Rich sector trans. If the trans has not been initialized
 before a default transformation of -20 deg theta rotation
 will be set.

 get Rich Mirror trans. If the trans has not been initialized
 before a default transformation 0 will be set.

 takes HMdcSeg object and calculates hits points on both
 modules in Lab cordinates (in cm !)

 calculates end points of a wire in Lab cordinates (in cm !)

 takes HMdcSeg object and calculates hit point on
 kickplane in Lab cordinates (in cm !)

 calc WALL hit point in LAB ccordinate sys (cm!)

 calc TOF hit point in LAB ccordinate sys (cm!)

 calc SHOWER hit point in LAB ccordinate sys (cm!)

 calc EMC Cluster point in LAB ccordinate sys (cm!)

 calc RPC cluster point in LAB ccordinate sys (cm!)

 calc RICH geant point (on Pad plane) in LAB ccordinate sys (cm!)

 calculates points on MDC layer to Lab cordinates (in cm !)

 calc WALL geant point (Module system) in LAB ccordinate sys (cm!)

 calc RPC geant point (Module system) in LAB ccordinate sys (cm!)

 calc SHOWER geant point (Module system) in LAB ccordinate sys (cm!)

 calc RPC geant point (Module system) in LAB ccordinate sys (cm!)

 calc vertex point in LAB coordinate sys (cm!)

 calculates Line from event vertex to MDCI
 with theta, phi from richhit. The points
 of the line are in LAB coordiante sys (cm!)

 calc the RICH frame of sector sec in LAB coordinate sys (cm!)
 transformation trans provides the theta rotation and offset to
 go to sector system. Phi rotation by sector gives LAB sys.

 calc the WALL frame in LAB coordinate sys (cm!)

 calc space coordinates of a RichPad in LAB coordinate sys
 transformation trans provides the theta rotation and offset to
 go to sector system. Phi rotation by sector gives LAB sys.

 calc space coordinates of a RichPad in LAB coordinate sys (!cm)
 transformation trans provides the theta rotation and offset to
 go to sector system. Phi rotation by sector gives LAB sys.

 calculates hit point of a line (represented by p1,p2, LAB [cm])
 with the RICH mirror. Result is returned in pout (LAB [cm])

 To calculate a line-sphere intersection  we need:
    * A ray with a known point of origin offset, and
      direction vector dir.
    * a sphere with a known centre at a point c and a
      known radius r
 Given the above mentioned sphere, a point p lies on the surface
 of the sphere if
 (p-c)*(p-c) = r^2
 Given a line with a point of origin offset, and a direction vector dir:
 line(t) = offset + t*dir  t > 0
 setting both equal
 (offset + t*dir - c)*(offset + t*dir - c) = r^2
 (dir*dir)*t^2 + 2*(offset-c)*dir*t + (offset-c)*(offset-c) - r^2 = 0
  == > At2 + Bt + C = 0
 where
   A = dir*dir
   B = 2(offset-c)*dir
   C =  (offset-c)*(offset-c) - r^2
 solve using quadratic formular
 no positive real root mean no intersection

 Simplification:
 If a sphere is centred at origin, a point p lies on a sphere
 of radius r2 if
 p * p = r^2
 we can find the t at which the (transformed) line
 (shifted by center vector c) intersects the sphere by
 (offset1 + t*dir) * (offset1 + t*dir) = r^2
 quadratic form :
 At2 + Bt + C = 0
 which now has coefficients:
    A = dir*dir
    B = 2(dir*offset1)
    C = offset1*offset1 - r^2

 There are two possible solutions to the quadratic equation:
 t_0 = (-B -\sqrt(B^2 - 4AC)) / 2A
 t_1 = (-B +\sqrt(B^2 - 4AC)) / 2A

 if the discriminant is negative, i.e. (B2 - 4AC) < 0,
 line has missed the sphere.
 To avoid poor numeric precision when B ~ \sqrt(B^2 - 4AC)
 t0 and t1 can be rewritten:
 t_0 = q/A
 t_1 = C/q
 where
 q = (-B + \sqrt(B^2 - 4AC)) / 2       B < 0
     (-B - \sqrt(B^2 - 4AC)) / 2       otherwise.

 The calculated hit point has to shifted back finally