#! /usr/bin/env python

def reference_to_physical_t3 ( t, n, ref ):

#*****************************************************************************80
#
## REFERENCE_TO_PHYSICAL_T3 maps a reference point to a physical point.
#
#  Discussion:
#
#    Given the vertices of an order 3 physical triangle and a point
#    (XSI,ETA) in the reference triangle, the routine computes the value
#    of the corresponding image point (X,Y) in physical space.
#
#    Note that this routine may also be appropriate for an order 6
#    triangle, if the mapping between reference and physical space
#    is linear.  This implies, in particular, that the sides of the
#    image triangle are straight and that the "midside" nodes in the
#    physical triangle are halfway along the sides of
#    the physical triangle.
#
#  Reference Element T3:
#
#    |
#    1  3
#    |  |\
#    |  | \
#    S  |  \
#    |  |   \
#    |  |    \
#    0  1-----2
#    |
#    +--0--R--1-->
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 July 2018
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real T(2,3), the coordinates of the vertices.  The vertices are assumed 
#    to be the images of (0,0), (1,0) and (0,1) respectively.
#
#    Input, integer N, the number of points to transform.
#
#    Input, real REF(2,N), the coordinates of points in the reference space.
#
#    Output, real PHY(2,N), the coordinates of the corresponding points in the 
#    physical space.
#
  import numpy as np

  phy = np.zeros ( [ 2, n ] )

  for i in range ( 0, 2 ):

    phy[i,:] = t[i,0] * ( 1.0 - ref[0,:] - ref[1,:] ) \
             + t[i,1] *         ref[0,:]              \
             + t[i,2] *                    ref[1,:]

  return phy

def reference_to_physical_t3_test ( ):

#*****************************************************************************80
#
## REFERENCE_TO_PHYSICAL_T3_TEST tests REFERENCE_TO_PHYSICAL_T3.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 July 2018
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_transpose_print import r8mat_transpose_print

  print ( '' )
  print ( 'REFERENCE_TO_PHYSICAL_T3_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  REFERENCE_TO_PHYSICAL_T3 maps points in a reference triangle' )
  print ( '  to points in a physical triangle.' )
 
  t = np.array ( [ \
    [ 2.0, 3.0, 0.0 ], \
    [ 0.0, 4.0, 3.0 ] ] )

  n = 3

  ref = np.array ( [ \
    [ 0.0, 1.0, 0.0 ], \
    [ 0.0, 0.0, 1.0 ] ] )

  r8mat_transpose_print ( 2, 3, t, '  XY triangle vertices:' )

  phy = reference_to_physical_t3 ( t, n, ref )

  print ( '' )
  print ( '  Apply map to RS triangle vertices.' )
  print ( '  Recover XY vertices (2,0), (3,4) and (0,3).' )
  print ( '' )

  for j in range ( 0, 3 ):
    print ( '  V(%d) = ( %g, %g )' % ( j, phy[0,j], phy[1,j] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'REFERENCE_TO_PHYSICAL_T3_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  reference_to_physical_t3_test ( )
  timestamp ( )