#! /usr/bin/env python
#
def polygon_centroid ( n, v ):

#*****************************************************************************80
#
## POLYGON_CENTROID computes the centroid of a polygon.
#
#  Discussion:
#
#    Denoting the centroid coordinates by CENTROID, then
#
#      CENTROID(1) = Integral ( Polygon interior ) x dx dy / Area ( Polygon )
#      CENTROID(2) = Integral ( Polygon interior ) y dx dy / Area ( Polygon ).
#
#    Green's theorem states that for continuously differentiable functions
#    M(x,y) and N(x,y),
#
#      Integral ( Polygon boundary ) ( M dx + N dy ) =
#      Integral ( Polygon interior ) ( dN/dx - dM/dy ) dx dy.
#
#    Using M(x,y) = 0 and N(x,y) = x^2/2, we get:
#
#      CENTROID(1) = 0.5 * Integral ( Polygon boundary ) x^2 dy
#                  / Area ( Polygon ),
#
#    which becomes
#
#      CENTROID(1) = 1/6 sum ( 1 <= I <= N )
#        ( X(I+1) + X(I) ) * ( X(I) * Y(I+1) - X(I+1) * Y(I))
#        / Area ( Polygon )
#
#    where, when I = N, the index "I+1" is replaced by 1.
#
#    A similar calculation gives us a formula for CENTROID(2).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 October 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Gerard Bashein and Paul Detmer,
#    Centroid of a Polygon,
#    Graphics Gems IV,
#    edited by Paul Heckbert,
#    AP Professional, 1994.
#
#  Parameters:
#
#    Input, integer N, the number of sides of the polygon.
#
#    Input, real V(2,N), the coordinates of the vertices.
#
#    Output, real CENTROID(2,1), the coordinates of the centroid.
#
  import numpy as np
  from i4_wrap import i4_wrap

  area = 0.0
  centroid = np.zeros ( 2 )

  for i in range ( 0, n ):

    ip1 = i4_wrap ( i + 1, 0, n - 1 )

    temp = ( v[0,i] * v[1,ip1] - v[0,ip1] * v[1,i] )

    area = area + temp

    centroid[0] = centroid[0] + ( v[0,ip1] + v[0,i] ) * temp
    centroid[1] = centroid[1] + ( v[1,ip1] + v[1,i] ) * temp

  area = area / 2.0

  if ( area == 0.0 ):
    centroid[0] = v[0]
    centroid[1] = v[1]
  else:
    centroid[0] = centroid[0] / ( 6.0 * area )
    centroid[1] = centroid[1] / ( 6.0 * area )

  return centroid

def polygon_centroid_test ( ):

#*****************************************************************************80
#
## POLYGON_CENTROID_TEST tests POLYGON_CENTROID.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    17 October 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_transpose_print import r8mat_transpose_print
  from r8vec_print import r8vec_print

  n = 4
  v = np.array ( [ \
    [ 1.0, 2.0, 1.0, 0.0 ], \
    [ 0.0, 1.0, 2.0, 1.0 ] ] )

  print ( '' )
  print ( 'POLYGON_CENTROID_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  POLYGON_CENTROID computes the centroid of a polygon.' )

  r8mat_transpose_print ( 2, n, v, '  The polygon vertices:' )

  centroid = polygon_centroid ( n, v )

  r8vec_print ( 2, centroid, '  POLYGON_CENTROID:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'POLYGON_CENTROID_TEST' )
  print ( '  Normal end of execution.' )
  return

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