#! /usr/bin/env python3
#
def triangle_contains_point ( T, p ):

#*****************************************************************************80
#
## triangle_contains_point() finds if a point is inside a triangle in 2D.
#
#  Discussion:
#
#    The routine assumes that the vertices are given in counter-clockwise
#    order.  If the triangle vertices are actually given in clockwise
#    order, this routine will behave as though the triangle contains
#    no points whatsoever!
#
#    The routine determines if a point P is "to the right of" each of the lines
#    that bound the triangle.  It does this by computing the cross product
#    of vectors from a vertex to its next vertex, and to P.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    23 October 2015
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real T(2,3), the triangle vertices.
#    The vertices should be given in counter clockwise order.
#
#    real P(2,1), the point to be checked.
#
#  Output:
#
#    logical INSIDE, is TRUE if the point is inside
#    the triangle or on its boundary.
#
  inside = True

  im1 = 2

  for i in range ( 0, 3 ):

    if ( 0.0 < ( p[0] - T[im1,0] ) * ( T[i,1] - T[im1,1] ) \
             - ( p[1] - T[im1,1] ) * ( T[i,0] - T[im1,0] ) ):
      inside = False
    im1 = i

  return inside

def triangle_contains_point_test ( ):

#*****************************************************************************80
#
## triangle_contains_point_test() tests triangle_contains_point().
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    07 June 2006
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  import platform

  print ( '' )
  print ( 'triangle_contains_point_test():' )
  print ( '  triangle_contains_point() reports if a point' )
  print ( '  is inside a triangle' )

  T = np.array ( [ \
    [ 0.10, 0.20 ],
    [ 0.85, 0.35 ],
    [ 0.25, 0.90 ] ] )

  print ( '' )
  print ( '  Triangle vertices:' )
  print ( T )

  plt.clf ( )
  plt.plot ( T[0:3,0], T[0:3,1], 'k-', linewidth = 3 )
  plt.plot ( [ T[2,0], T[0,0] ], [ T[2,1], T[0,1] ],'k-', linewidth = 3 )

  for j in range ( 0, 100 ):
    p = np.random.rand ( 2 )
    if triangle_contains_point ( T, p ):
      plt.plot ( p[0], p[1], 'bo' )
    else:
      plt.plot ( p[0], p[1], 'ro' )

  plt.axis ( 'equal' )
  plt.grid ( True )
  plt.title ( 'Blue points inside, red outside' )
  filename = 'triangle_contains_point.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.show ( )

  return

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