#! /usr/bin/env python
#
def triangle_reference_sample ( n, seed ):

#*****************************************************************************80
#
## TRIANGLE_REFERENCE_SAMPLE returns random points in the reference triangle.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 November 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of points to generate.
#
#    Input, integer SEED, a seed for the random number generator.
#
#    Output, real P(2,N), random points in the triangle.
#
#    Output, integer SEED, a seed for the random number generator.
#
  import numpy as np
  from r8vec_uniform_01 import r8vec_uniform_01

  alpha, seed = r8vec_uniform_01 ( n, seed )
#
#  Interpret R as a percentage of the triangle's area.
#
#  Imagine a line L, parallel to side 1, so that the area between
#  vertex 1 and line L is R percent of the full triangle's area.
#
#  The line L will intersect sides 2 and 3 at a fraction
#  ALPHA = SQRT ( R ) of the distance from vertex 1 to vertices 2 and 3.
#
  for i in range ( 0, n ):
    alpha[i] = np.sqrt ( alpha[i] )
#
#  Now choose, uniformly at random, a point on the line L.
#
  beta, seed = r8vec_uniform_01 ( n, seed )

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

  for j in range ( 0, n ):
    p[0,j] = ( 1.0 - beta[j] ) * alpha[j]
    p[1,j] =         beta[j]   * alpha[j]

  return p, seed

def triangle_reference_sample_test ( ):

#*****************************************************************************80
#
## TRIANGLE_REFERENCE_SAMPLE_TEST tests TRIANGLE_REFERENCE_SAMPLE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 November 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_transpose_print import r8mat_transpose_print
  from triangle_xy_to_xsi import triangle_xy_to_xsi

  seed = 123456789
  t = np.array ( [ \
    [ 0.0, 1.0,  0.0 ], \
    [ 0.0, 0.0,  1.0 ] ] )

  print ( '' )
  print ( 'TRIANGLE_REFERENCE_SAMPLE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TRIANGLE_REFERENCE_SAMPLE samples the reference triangle.' )

  r8mat_transpose_print ( 2, 3, t, '  Triangle vertices:' )

  print ( '' )
  print ( '  Sample points (X,Y) and (XSI1,XSI2,XSI3) coordinates:' )
  print ( '' )

  for i in range ( 0, 10 ):

    p, seed = triangle_reference_sample ( 1, seed )

    xsi = triangle_xy_to_xsi ( t, p )

    print ( '  %10g  %10g    %10g  %10g  %10g' % ( p[0], p[1], xsi[0], xsi[1], xsi[2] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRIANGLE_REFERENCE_SAMPLE_TEST' )
  print ( '  Normal end of execution.' )
  return

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