angle_rad_3d.f90

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FUNCTION angle_rad_3d ( x1, y1, z1, x2, y2, z2, x3, y3, z3 )

!!****f* Rocfrac/Source/angle_rad_3d.f90
!!
!!  NAME
!!     angle_rad_3d
!!
!!  FUNCTION
!!     returns the angle in radians between two rays in 3D.
!!
!!  NOTES
!!
!!    The routine always computes the SMALLER of the two angles between
!!    two rays.  Thus, if the rays make an (exterior) angle of 
!!    1.5 radians, the (interior) angle of 0.5 radians will be reported.
!!
!!  Formula:
!!
!!    X dot Y = Norm(X) * Norm(Y) * Cos ( Angle(X,Y) )

!!  INPUTS
!!    real X1, Y1, Z1, X2, Y2, Z2, X3, Y3, Z3, are three points
!!    which define the rays.  The rays are:
!!    ( X1-X2, Y1-Y2, Z1-Z2 ) and ( X3-X2, Y3-Y2, Z3-Z2 ).
!!  
!!  OUTPUT
!!    real ANGLE_RAD_3D, the angle between the two rays, in radians.
!!    This value will always be between 0 and PI.  If either ray has 
!!    zero length, then the angle is returned as zero.
!!
!!***

  REAL*8 angle_rad_3d
  REAL*8 dot
  REAL*8 dot0_3d
  REAL*8 enorm0_3d
  REAL*8 v1norm
  REAL*8 v2norm
  REAL*8 x1
  REAL*8 x2
  REAL*8 x3
  REAL*8 y1
  REAL*8 y2
  REAL*8 y3
  REAL*8 z1
  REAL*8 z2
  REAL*8 z3

! computes the dot product of (P1-P0) and (P2-P0) in 3D.

  dot =  ( x1 - x2 ) * ( x3 - x2 ) + ( y1 - y2 ) * ( y3 - y2 ) + &
       ( z1 - z2 ) * ( z3 - z2 )
!
!  computes the Euclidean norm of (Point1-Point0) in 3D.

  v1norm = sqrt( ( x2 - x1 )**2 + ( y2 - y1 )**2 + ( z2 - z1 )**2 )
  v2norm = sqrt( ( x2 - x3 )**2 + ( y2 - y3 )**2 + ( z2 - z3 )**2 )
  
  IF ( v1norm == 0.d0 .OR. v2norm == 0.d0 ) THEN
     angle_rad_3d = 0.d0
  ELSE
     angle_rad_3d = acos( dot / ( v1norm * v2norm ) )
  END IF
  
  RETURN
END FUNCTION angle_rad_3d