#! /usr/bin/env python
#
def uniform_in_triangle_map1 ( v1, v2, v3, n, seed ):

#*****************************************************************************80
#
## UNIFORM_IN_TRIANGLE_MAP1 maps uniform points into a triangle.
#
#  Discussion:
#
#    The triangle is defined by three vertices.  This routine
#    uses Turk's rule #1.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    19 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Greg Turk,
#    Generating Random Points in a Triangle,
#    in Graphics Gems,
#    edited by Andrew Glassner,
#    AP Professional, 1990, pages 24-28.
#
#  Parameters:
#
#    Input, real V1(2), V2(2), V3(2), the vertices.
#
#    Input, integer N, the number of points.
#
#    Input/output, integer SEED, a seed for the random number generator.
#
#    Output, real X(2,N), the points.
#
  import numpy as np
  from r8vec_uniform_01 import r8vec_uniform_01

  x = np.zeros ( [ 2, n ] )
#
#  Generate the points using Turk's rule 1.
#
  for j in range ( 0, n ):

    r, seed = r8vec_uniform_01 ( 2, seed )

    a = 1.0 - np.sqrt ( r[1] )
    b = ( 1.0 - r[0] ) * np.sqrt ( r[1] )
    c = r[0] * np.sqrt ( r[1] )

    for i in range ( 0, 2 ):
      x[i,j] = ( a * v1[i] \
               + b * v2[i] \
               + c * v3[i] )

  return x, seed

def uniform_in_triangle_map1_test ( ):

#*****************************************************************************80
#
#% UNIFORM_IN_TRIANGLE_MAP1_TEST tests UNIFORM_IN_TRIANGLE_MAP1.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 January 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_transpose_write import r8mat_transpose_write

  n = 1000
  seed = 123456789
  v1 = np.array ( [ 0.75, 0.90 ] )
  v2 = np.array ( [ 0.00, 0.20 ] )
  v3 = np.array ( [ 0.95, 0.65 ] )

  print ( '' )
  print ( 'UNIFORM_IN_TRIANGLE_MAP1_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  UNIFORM_IN_TRIANGLE_MAP1 maps uniform' )
  print ( '  points into a triangle.' )
  print ( '' )
  print ( '  Number of points N =          %d' % ( n ) )
  print ( '  Initial random number SEED =  %d' % ( seed ) )

  print ( '' )
  print ( '  V1 = %12f  %12f' % ( v1[0], v1[1] ) )
  print ( '  V2 = %12f  %12f' % ( v2[0], v2[1] ) )
  print ( '  V3 = %12f  %12f' % ( v3[0], v3[1] ) )

  x, seed = uniform_in_triangle_map1 ( v1, v2, v3, n, seed )

  print ( '  Final random number SEED =    %d' % ( seed ) )

  filename = 'uniform_in_triangle_map1.txt'
  r8mat_transpose_write ( filename, 2, n, x )

  print ( '' )
  print ( '  Data written to "%s".' % ( filename ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'UNIFORM_IN_TRIANGLE_MAP1_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  uniform_in_triangle_map1_test ( )
  timestamp ( )