13.2.10} lattic.f (symmetry transformation for lattice geometry)

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 Subroutine LATTIC is activated by one or more LATTICE cards in the
 geometry input (see 8}). It is expected to transform coordinates and
 direction cosines from any lattice cell (defined by card LATTICE) to
 the reference system in which the basic structure has been described.
 The user is expected to provide a transformation of coordinates and
 vector direction cosines from each lattice cell to the corresponding
 basic structure (in ENTRY LATTIC) and of direction cosines from the
 basic structure to each corresponding lattice cell (in ENTRY LATNOR).

 Entries:

 * LATTIC  (position and direction symmetry transformation from lattice
   cell to prototype structure)
     Argument list:
          XB(1), XB(2), XB(3) : actual physical position coordinates in IRLTGG
                                lattice cell
          WB(1), WB(2), WB(3) : actual physical direction cosines in IRLTGG
                                lattice cell
          DIST                : current step length
          SB(1), SB(2), SB(3) : transformed coordinates in prototype cell
          UB(1), UB(2), UB(3) : transformed cosines in prototype cell
          IR                  : region number in prototype cell
          IRLTGG              : lattice cell number
          IRLT                : array containing region indices corresponding to
                                lattice cells
          IFLAG               : reserved variable

   LATTIC returns the tracking point coordinates (SB) and direction
   cosines(UB) in the reference prototype geometrical structure,
   corresponding to real position/direction XB, WB in the actual cell
   IRLTGG (defined as input region IR by a LATTICE card).
   When the lattice option is activated, the tracking proceeds in two
   different systems: the "real" one, and that of the basic symmetry unit.
   Particle positions and directions are swapped from their real values
   to their symmetric ones in the basic cell, to perform the physical
   transport in the regions and materials that form the prototype
   geometrical structure and back again to the real world. The
   correspondence between "real" and "basic" position/direction depends
   on the symmetry transformation and on the lattice cell number.

 * LATNOR (LATtice cell NORmal transformation from prototype structure to
   lattice cell)
     Argument list:
          UN(1), UN(2), UN(3) : direction cosines of the vector normal to the
                                surface, in the prototype cell (entry values)
                                and in the lattice cell (returned values)
          IRLTNO              : present lattice cell number

   Entry LATNOR transforms the direction cosines stored in the vector
   UN(3) from the system of the basic prototype unit to that of the real
   world in lattice cell number IRLTNO. Therefore, this cosine
   transformation must be the inverse of that performed on the cosines by
   the LATTIC entry: but while LATTIC maps vector UB to a different
   vector WB, LATNOR maps the UN vector to itself.
   Note that if the transformation implies a rotation, it is necessary to
   save first the incoming UN cosines to local variables, to avoid
   overwriting the vector before all transformation statements are executed.

 
Notes:
     Different symmetry transformations can of course be implemented
     in the same LATTIC routine (each being activated by a different cell
     number or range of cell numbers).
     The advantage of the lattice geometry is to avoid describing in detail
     the geometry of repetitive multi-modular structures. It must be
     realised, however, that a penalty is generally paid in computer efficiency.
     Also, a region contained in the prototype cell and all those "mapped"
     to it inside lattice cells are treated by the program as if they
     were connected with "non-overlapping ORs" into a single region.
     Therefore, any region-based scoring (options SCORE, USRTRACK, etc.)
     can only provide quantities averaged over the whole structure. More
     detailed information must be obtained by region-independent options
     such as USRBIN or by user-written routines (MGDRAW).
     The USRBIN and EVENTBIN options, with 
WHAT(1)
 = 8, can also be used
     to request a special binning type which activates the MUSRBR,
     LUSRBL, FUSRBV user routines to recover lattice information (see
     routine musrbr.f below)
     A transformation between a lattice cell and a prototype region can
     alternatively be defined without resorting to the LATTIC user routine.
     In this case, the transformation is defined via a ROT-DEFIni card and
     the correspondence is established by giving the transformation index
     in the 
SDUM
 of the LATTICE card (see Chap. 8}).

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