#! /usr/bin/env python3
#
def r83col_print_part ( n, a, max_print, title ):

#*****************************************************************************80
#
## r83col_print_part() prints "part" of an R83COL.
#
#  Discussion:
#
#    An R83COL is a (3,N) array of R8's.
#
#    The user specifies MAX_print, the maximum number of lines to print.
#
#    If N, the size of the vector, is no more than MAX_print, then
#    the entire vector is printed, one entry per line.
#
#    Otherwise, if possible, the first MAX_print-2 entries are printed,
#    followed by a line of periods suggesting an omission,
#    and the last entry.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    11 April 2015
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer N, the number of entries of the vector.
#
#    real A(N,3), the vector to be printed.
#
#    integer MAX_print, the maximum number of lines
#    to print.
#
#    string TITLE, a title.
#
  if ( 0 < max_print ):

    if ( 0 < n ):

      if ( 0 < len ( title ) ):
        print ( '' )
        print ( title )

      print ( '' )

      if ( n <= max_print ):

        for i in range ( 0, n ):
          print ( '  %4d  %14g  %14g  %14g' % ( i, a[i,0], a[i,1], a[i,2] ) )
 
      elif ( 3 <= max_print ):

        for i in range ( 0, max_print - 2 ):
          print ( '  %4d  %14g  %14g  %14g' % ( i, a[i,0], a[i,1], a[i,2] ) )
        print ( '  ....  ..............  ..............  ..............' )
        i = n - 1
        print ( '  %4d  %14g  %14g  %14g' % ( i, a[i,0], a[i,1], a[i,2] ) )

      else:

        for i in range ( 0, max_print - 1 ):
          print ( '  %4d  %14g  %14g  %14g' % ( i, a[i,0], a[i,1], a[i,2] ) )
        i = max_print - 1
        print ( '  %4d  %14g  %14g  %14g  ...more entries...' \
          % ( i, a[i,0], a[i,1], a[i,2] ) )

  return

def r83col_print_part_test ( ):

#*****************************************************************************80
#
## r83col_print_part_test tests r83col_print_part.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    11 April 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'r83col_print_part_test' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  r83col_print_part prints part of an R83COL.' )

  n = 10

  v = np.array ( [ \
    [  11,  12,  13 ], \
    [  21,  22,  23 ], \
    [  31,  32,  33 ], \
    [  41,  42,  43 ], \
    [  51,  52,  53 ], \
    [  61,  62,  63 ], \
    [  71,  72,  73 ], \
    [  81,  82,  83 ], \
    [  91,  92,  93 ], \
    [ 101, 102, 103 ] ] )

  max_print = 2
  r83col_print_part ( n, v, max_print, '  Output with MAX_print = 2' )

  max_print = 5
  r83col_print_part ( n, v, max_print, '  Output with MAX_print = 5' )

  max_print = 25
  r83col_print_part ( n, v, max_print, '  Output with MAX_print = 25' )
#
#  Terminate.
#
  print ( '' )
  print ( 'r83col_print_part_test:' )
  print ( '  Normal end of execution.' )
  return

def r8mat_write ( filename, m, n, a ):

#*****************************************************************************80
#
## r8mat_write writes an R8MAT to a file.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    12 October 2014
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    string FILENAME, the name of the output file.
#
#    integer M, the number of rows in A.
#
#    integer N, the number of columns in A.
#
#    real A(M,N), the matrix.
#
  output = open ( filename, 'w' )

  for i in range ( 0, m ):
    for j in range ( 0, n ):
      s = '  %g' % ( a[i,j] )
      output.write ( s )
    output.write ( '\n' )

  output.close ( )

  return

def r8mat_write_test ( ):

#*****************************************************************************80
#
## r8mat_write_test tests r8mat_write.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    12 October 2014
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'r8mat_write_test:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test r8mat_write, which writes an R8MAT to a file.' )

  filename = 'r8mat_write_test.txt'
  m = 5
  n = 3
  a = np.array ( (  \
    ( 1.1, 1.2, 1.3 ), \
    ( 2.1, 2.2, 2.3 ), \
    ( 3.1, 3.2, 3.3 ), \
    ( 4.1, 4.2, 4.3 ), \
    ( 5.1, 5.2, 5.3 ) ) )
  r8mat_write ( filename, m, n, a )

  print ( '' )
  print ( '  Created file "%s".' % ( filename ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'r8mat_write_test:' )
  print ( '  Normal end of execution.' )
  return
  
def tetrahedron_grid_count ( n ):

#*****************************************************************************80
#
## tetrahedron_grid_count counts the grid points inside a tetrahedron.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer N, the number of subintervals.
#
#  Output:
#
#    integer NG, the number of grid points.
#
  ng = ( ( n + 1 ) * ( n + 2 ) * ( n + 3 ) ) // 6

  return ng

def tetrahedron_grid_count_test ( ):

#*****************************************************************************80
#
## tetrahedron_grid_count_test tests tetrahedron_grid_count.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'tetrahedron_grid_count_test:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  tetrahedron_grid_count can count the points in a grid' )
  print ( '  with N+1 points on a side, based on any tetrahedron.' )

  print ( '' )
  print ( '     N        NG' )
  print ( '' )

  for n in [ 1, 2, 3, 4, 5, 10, 15, 20, 25, 50, 100 ]:
    ng = tetrahedron_grid_count ( n )
    print ( '  %4d  %8d' % ( n, ng ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'tetrahedron_grid_count_test:' )
  print ( '  Normal end of execution.' )
  return

def tetrahedron_grid_display ( xv, ng, xg, filename ):

#*****************************************************************************80
#
## tetrahedron_grid_display displays grid points inside a tetrahedron.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real XV[4,3], the vertices.
#
#    integer NG, the number of grid points.
#
#    real XG[NG,3], the grid points.
#
#    string FILENAME, the name of the plotfile to be created.
#
  import matplotlib.pyplot as plt
  from mpl_toolkits.mplot3d import Axes3D

  fig = plt.figure ( )
  ax = fig.add_subplot ( 111, projection = '3d' )
#
#  Draw the grid points.
#
  ax.scatter ( xg[:,0], xg[:,1], xg[:,2], 'b' )
#
#  Outline the region by its edges.
#
  ax.plot ( [ xv[0,0], xv[1,0] ], [ xv[0,1], xv[1,1] ], [ xv[0,2], xv[1,2] ], 'r' )
  ax.plot ( [ xv[0,0], xv[2,0] ], [ xv[0,1], xv[2,1] ], [ xv[0,2], xv[2,2] ], 'r' )
  ax.plot ( [ xv[0,0], xv[3,0] ], [ xv[0,1], xv[3,1] ], [ xv[0,2], xv[3,2] ], 'r' )
  ax.plot ( [ xv[1,0], xv[2,0] ], [ xv[1,1], xv[2,1] ], [ xv[1,2], xv[2,2] ], 'r' )
  ax.plot ( [ xv[1,0], xv[3,0] ], [ xv[1,1], xv[3,1] ], [ xv[1,2], xv[3,2] ], 'r' )
  ax.plot ( [ xv[2,0], xv[3,0] ], [ xv[2,1], xv[3,1] ], [ xv[2,2], xv[3,2] ], 'r' )

  ax.set_xlabel ( '<---X--->' )
  ax.set_ylabel ( '<---Y--->' )
  ax.set_zlabel ( '<---Z--->' )
  ax.set_title ( 'Grid points in tetrahedron' )
  ax.grid ( True )
# ax.axis ( 'equal' )

  plt.savefig ( filename )
  plt.show ( block = False )
  plt.close ( )

  return

def tetrahedron_grid_display_test ( ):

#*****************************************************************************80
#
## tetrahedron_grid_display displays grid points inside a tetrahedron.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'tetrahedron_grid_display_test:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  tetrahedron_grid_display can display a grid of points in a tetrahedron.' )

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

  ng = 10
  xg = np.array ( [ \
    [  0.0,  0.0,  0.0 ], \
    [  1.0,  0.0,  0.0 ], \
    [  2.0,  0.0,  0.0 ], \
    [  0.0,  1.0,  0.0 ], \
    [  0.0,  2.0,  0.0 ], \
    [  1.0,  1.0,  0.0 ], \
    [  0.0,  0.0,  1.0 ], \
    [  1.0,  0.0,  1.0 ], \
    [  0.0,  1.0,  1.0 ], \
    [  0.0,  0.0,  2.0 ] ] )

  filename = 'tetrahedron_grid_display.png'

  tetrahedron_grid_display ( xv, ng, xg, filename )
#
#  Terminate.
#
  print ( '' )
  print ( 'tetrahedron_grid_display_test:' )
  print ( '  Normal end of execution.' )
  return
  
def tetrahedron_grid_points ( n, xv, ng ):

#*****************************************************************************80
#
## tetrahedron_grid_points computes points on a tetrahedral grid.
#
#  Discussion:
#
#    The grid is defined by specifying the coordinates of an enclosing
#    tetrahedron T, and the number of subintervals each edge of the 
#    tetrahedron should be divided into.
#
#    Choosing N = 10, for instance, breaks each side into 10 subintervals,
#    and produces a grid of ((10+1)*(10+2)*(10+3))/6 = 286 points.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer N, the number of subintervals.
#
#    real XV[4,3], the vertices of the tetrahedron.
#
#    integer NG, the number of grid points.
#
#  Output:
#
#    real XG[NG,3], the tetrahedron grid points.
#
  import numpy as np

  xg = np.zeros ( [ ng, 3 ] )

  p = 0

  for i in range ( 0, n + 1 ):
    for j in range ( 0, n + 1 - i ):
      for k in range ( 0, n + 1 - i - j ):
        l = n - i - j - k
        xg[p,0] = ( float ( i ) * xv[0,0] + float ( j ) * xv[1,0] \
                  + float ( k ) * xv[2,0] + float ( l ) * xv[3,0] ) / float ( n )
        xg[p,1] = ( float ( i ) * xv[0,1] + float ( j ) * xv[1,1] \
                  + float ( k ) * xv[2,1] + float ( l ) * xv[3,1] ) / float ( n )
        xg[p,2] = ( float ( i ) * xv[0,2] + float ( j ) * xv[1,2] \
                  + float ( k ) * xv[2,2] + float ( l ) * xv[3,2] ) / float ( n )
        p = p + 1

  return xg

def tetrahedron_grid_points_test ( ):

#*****************************************************************************80
#
## tetrahedron_grid_points_test tests tetrahedron_grid_points.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    10 November 2011
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'tetrahedron_grid_points_test:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  tetrahedron_grid_points can define a tetrahedral grid' )
  print ( '  with N+1 points on a side, based on any tetrahedron.' )

  n = 5
  print ( '  N = %d' % ( n ) )

  ng = tetrahedron_grid_count ( n )
#
#  Define the tetrahedron vertices.
#
  xv = np.array ( [ \
    [ 0.0, 0.0, 0.0 ], \
    [ 2.0, 1.0, 0.0 ], \
    [ 1.0, 4.0, 0.0 ], \
    [ 3.0, 3.0, 3.0 ] ] )

  r83col_print_part ( 4, xv, 20, '  Tetrahedron vertices:' )

  xg = tetrahedron_grid_points ( n, xv, ng )

  r83col_print_part ( ng, xg, 20, '  Tetrahedron grid points:' )
#
#  Write the data to a file.
#
  filename = 'tetrahedron_grid_points.xyz'

  r8mat_write ( filename, ng, 3, xg )

  print ( '' )
  print ( '  Data written to the file "%s".' % ( filename ) )
#
#  Plot the data.
#
  filename = 'tetrahedron_grid_points.png'
  tetrahedron_grid_display ( xv, ng, xg, filename )

  print ( '' )
  print ( '  Plot written to the file "%s".' % ( filename ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'tetrahedron_grid_points_test:' )
  print ( '  Normal end of execution.' )
  return

def tetrahedron_grid_test ( ):

#*****************************************************************************80
#
## tetrahedron_grid_test() tests tetrahedron_grid().
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'tetrahedron_grid_test():' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test tetrahedron_grid().' )
#
#  Utilities:
#
  r83col_print_part_test ( )
  r8mat_write_test ( )
#
#  Library.
#
  tetrahedron_grid_count_test ( )
  tetrahedron_grid_display_test ( )
  tetrahedron_grid_points_test ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'tetrahedron_grid_test():' )
  print ( '  Normal end of execution.' )
  return

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    06 April 2013
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return None

if ( __name__ == '__main__' ):
  timestamp ( )
  tetrahedron_grid_test ( )
  timestamp ( )