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

#*****************************************************************************80
#
## POLYGON_AREA computes the area of a polygon.
#
#  Discussion:
#
#    AREA = 1/2 * abs ( sum ( 1 <= I <= N ) X(I) * ( Y(I+1) - Y(I-1) ) )
#    where Y(0) should be replaced by Y(N), and Y(N+1) by Y(1).
#
#    If the vertices are given in counterclockwise order, the area
#    will be positive.  If the vertices are given in clockwise order,
#    the area will be negative.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 October 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of vertices of the polygon.
#
#    Input, real V(2,N), the vertices.
#
#    Output, real AREA, the area of the polygon.
#
  from i4_wrap import i4_wrap

  area = 0.0

  for i in range ( 0, n ):

    im1 = i4_wrap ( i - 1, 0, n - 1 )
    ip1 = i4_wrap ( i + 1, 0, n - 1 )

    area = area + v[0,i] * ( v[1,ip1] - v[1,im1] )

  area = 0.5 * area;

  return area

def polygon_area_test ( ):

#*****************************************************************************80
#
## POLYGON_AREA_TEST tests POLYGON_AREA.
#
#  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

  test_num = 2
  area_exact_test = np.array ( [ 2.0, 6.0 ] )
  n_test = np.array ( [ 4, 8 ] )

  print ( '' )
  print ( 'POLYGON_AREA_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  POLYGON_AREA computes the area of a polygon.' )

  for test in range ( 0, test_num ):

    n = n_test[test]
    area_exact = area_exact_test[test]

    if ( test == 0 ):

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

    elif ( test == 1 ):

      v = np.array ( [ \
        [ 0.0, 3.0, 3.0, 2.0, 2.0, 1.0, 1.0, 0.0 ], \
        [ 0.0, 0.0, 3.0, 3.0, 1.0, 1.0, 2.0, 2.0 ] ] )

    print ( '' )
    print ( '  Number of polygonal vertices = %d' % ( n ) )

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

    area = polygon_area ( n, v )

    print ( '' )
    print ( '  Exact area is        %g' % ( area_exact ) )
    print ( '  The computed area is %g' % ( area ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'POLYGON_AREA_TEST' )
  print ( '  Normal end of execution.' )
  return

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