def triangle_distance ( ):

#*****************************************************************************80
#
## triangle_distance() histograms distances between random triangle points.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    30 January 2025
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np

  n = 10000
#
#  345 right triangle.
#
  t = np.array ( [ \
    [ 0.00, 0.00 ], \
    [ 3.00, 0.00 ], \
    [ 0.00, 4.00 ]  \
  ] )
#
#  Randomly sample n pairs of points in the triangle.
#
  p = triangle_sample ( t, n )
  q = triangle_sample ( t, n )
#
#  Compute all the distances.
#
  d = ( p - q ) ** 2
  d = np.sum ( d, axis = 1 )
  d = np.sqrt ( d )
  d_max = np.max ( d )
#
#  Make a histogram.
#
  plt.hist ( d, bins = 20, rwidth = 0.95, density = True )
  plt.grid ( True )
  plt.xlabel ( '<-- Distance -->' )
  plt.ylabel ( '<-- Frequency -->' )
  plt.title ( 'Distances between random points in a 3/4/5 triangle' )
  filename = 'triangle_distance.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.show ( )
  plt.close ( )

  return

def triangle_sample ( t, n ):

#*****************************************************************************80
#
## triangle_sample() uniformly samples a triangle.
#
#  Discussion:
#
#    The triangle is defined by three vertices.  This routine
#    uses Turk's rule #2.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    30 January 2025
#
#  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.
#
#  Input:
#
#    real T(3,2), the X and Y coordinates of the vertices.
#
#    integer N, the number of points desired.
#
#  Output:
#
#    real X(N,2), the points.
#
  import numpy as np
#
#  Choose N random pairs of values in [0,1].
#
  s = np.random.random ( [ n, 2 ] )
#
#  We want these pairs to be inside the unit triangle.
#  If 1 < s0 + s1, replace by 1-s0 and 1-s1.
#
  i = 1.0 < s[:,0] + s[:,1]
  s[i,:] = 1.0 - s[i,:]
#
#  Use S to compute barycentric coordinates R.
#
  r = np.zeros ( [ n, 3 ] )
  r[:,0] = s[:,0]
  r[:,1] = s[:,1]
  r[:,2] = 1.0 - r[:,0] - r[:,1]
#
#  X[N,2] = R[N,3] * T[3,2]
#
  x = np.matmul ( r, t )

  return x

if ( __name__ == "__main__" ):
  triangle_distance ( )