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MATGT

       SUBROUTINE  MATGT (T, ERROR,
      X                   OX,OY,OZ, UX,UY,UZ, VX,VY,VZ, WX,WY,WZ,
      X                   OU,OV,OW, UU,UV,UW, VU,VV,VW, WU,WV,WW,
      X                   NRMXYZ,NRMUVW)
 C$    (General 4-Dimensional Transformation)
 C$    Given 4 non-coplanar points in the (X,Y,Z) world coordinate
 C$    system, compute  a transformation  matrix which  maps  them
 C$    into 4 other  non-coplanar points in  a (U,V,W)  coordinate
 C$    system.  For convenience, three of the points are expressed
 C$    relative to the fourth  which will form  the origin of  the
 C$    (U,V,W) coordinate system.  One would typically map (U,V,W)
 C$    axis unit vectors expressed in the (X,Y,Z) system into unit
 C$    vectors  in   the   (U,V,W)  system.    Thus,   again   for
 C$    convenience,  three  of  the  points  in  each  system  may
 C$    optionally be renormalized internally to unit vectors.  The
 C$    arguments are:
 C$
 C$    T(*,*)..............4-dimensional transformation matrix
 C$                        returned.
 C$    ERROR...............LOGICAL flag set .TRUE. on return if
 C$                        a transformation matrix could not be
 C$                        computed.  A unit matrix is returned in
 C$                        T(*,*) if this is the case.
 C$    (OX,OY,OZ)..........Coordinates of (U,V,W) coordinate
 C$                        system origin measured in (X,Y,Z)
 C$                        system.
 C$    (UX,UY,UZ)..........(X,Y,Z) coordinates of point U relative
 C$                        to (OX,OY,OZ).
 C$    (VX,VY,VZ)..........(X,Y,Z) coordinates of point V relative
 C$                        to (OX,OY,OZ).
 C$    (WX,WY,WZ)..........(X,Y,Z) coordinates of point W relative
 C$                        to (OX,OY,OZ).
 C$    (OU,OV,OW)..........(U,V,W) coordinates of (U,V,W)
 C$                        coordinate system  origin.   These  are
 C$                        normally (0,0,0).
 C$    (UU,UV,UW)..........(U,V,W) coordinates of point U relative
 C$                        to (OU,OV,OW).
 C$    (VU,VV,VW)..........(U,V,W) coordinates of point V relative
 C$                        to (OU,OV,OW).
 C$    (WU,WV,WW)..........(U,V,W) coordinates of point W relative
 C$                        to (OU,OV,OW).
 C$    NRMXYZ..............LOGICAL flag which is .TRUE. if the
 C$                        vectors U,  V,  and W  in  the  (X,Y,Z)
 C$                        system    are    to    be    internally
 C$                        renormalized to unity.
 C$    NRMUVW..............LOGICAL flag which is .TRUE. if the
 C$                        vectors U,  V,  and W  in  the  (U,V,W)
 C$                        system    are    to    be    internally
 C$                        renormalized to unity.
 C$
 C$    While the point O will  normally be the (U,V,W) origin,  it
 C$    may also be any other convenient reference point.
 C$    (10-OCT-84)