#! /usr/bin/env python
#
def sphere_llt_grid_line_count ( lat_num, long_num ):

#*****************************************************************************80
#
## SPHERE_LLT_GRID_LINE_COUNT counts lines for an LLT grid on a sphere.
#
#  Discussion:
#
#    A SPHERE LLT grid imposes a grid of triangles on a sphere,
#    using latitude and longitude lines.
#
#    The number returned is the number of pairs of points to be connected
#    to form all the line segments.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    21 May 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer LAT_NUM, LONG_NUM, the number of latitude and
#    longitude lines to draw.  The latitudes do not include the North and South
#    poles, which will be included automatically, so LAT_NUM = 5, for instance,
#    will result in points along 7 lines of latitude.
#
#    Output, integer LINE_NUM, the number of grid lines.
#
  line_num = long_num * ( lat_num + 1 ) \
           + long_num *   lat_num \
           + long_num * ( lat_num - 1 )

  return line_num

def sphere_llt_grid_line_count_test ( ):

#*****************************************************************************80
#
## SPHERE_LLT_GRID_LINE_COUNT_TEST tests SPHERE_LLT_GRID_LINE_COUNT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    21 May 2015
#
#  Author:
#
#    John Burkardt
#
  lat_num = 3
  long_num = 4

  print ''
  print 'SPHERE_LLT_GRID_LINE_COUNT_TEST'
  print '  SPHERE_LLT_GRID_LINE_COUNT counts the lines used for a'
  print '  grid based on triangles defined by latitude and longitude'
  print '  lines on a sphere in 3D.'
  print ''
  print '     LAT_NUM    LONG_NUM   LINE_NUM'

  for lat_num in range ( 1, 19, 2 ):
    print ''
    long_num = 1
    for long_log in range ( 1, 5 ):
      long_num = long_num * 2
      line_num = sphere_llt_grid_line_count ( lat_num, long_num )
      print '  %8d  %8d  %8d' % ( lat_num, long_num, line_num )
#
#  Terminate.
#
  print ''
  print 'SPHERE_LLT_GRID_LINE_COUNT_TEST:'
  print '  Normal end of execution.'

  return

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