function [ adj_num, adj_col ] = triangulation_order6_adj_count ( node_num, ...
  tri_num, triangle_node, triangle_neighbor )

%*****************************************************************************80
%
%% TRIANGULATION_ORDER6_ADJ_COUNT counts adjacencies in a triangulation.
%
%  Discussion:
%
%    This routine is called to count the adjacencies, so that the
%    appropriate amount of memory can be set aside for storage when
%    the adjacency structure is created.
%
%    The triangulation is assumed to involve 6-node triangles.
%
%    Two nodes are "adjacent" if they are both nodes in some triangle.
%    Also, a node is considered to be adjacent to itself.
%
%  Diagram:
%
%       3
%    s  |\
%    i  | \
%    d  |  \
%    e  6   5  side 2
%       |    \
%    3  |     \
%       |      \
%       1---4---2
%
%         side 1
%
%    The local node numbering
%
%
%   21-22-23-24-25
%    |\    |\    |
%    | \   | \   |
%   16 17 18 19 20
%    |   \ |   \ |
%    |    \|    \|
%   11-12-13-14-15
%    |\    |\    |
%    | \   | \   |
%    6  7  8  9 10
%    |   \ |   \ |
%    |    \|    \|
%    1--2--3--4--5
%
%    A sample grid.
%
%
%    Below, we have a chart that lists the nodes adjacent to each node, with 
%    an asterisk to indicate the adjacency of the node to itself
%    (in some cases, you want to count this self adjacency and in some
%    you don't).
%
%    N   Adjacencies
%
%    1:  *  2  3  6  7 11
%    2:  1  *  3  6  7 11
%    3:  1  2  *  4  5  6  7  8  9 11 12 13
%    4:  3  *  5  8  9 13
%    5:  3  4  *  8  9 10 13 14 15
%    6:  1  2  3  *  7 11
%    7:  1  2  3  6  *  8 11 12 13
%    8:  3  4  5  7  *  9 11 12 13
%    9:  3  4  5  8  * 10 13 14 15
%   10:  5  9  * 13 14 15
%   11:  1  2  3  6  7  8  * 12 13 16 17 21
%   12:  3  7  8 11  * 13 16 17 21
%   13:  3  4  5  7  8  9 10 11 12  * 14 15 16 17 18 19 21 22 23
%   14:  5  9 10 13  * 15 18 19 23
%   15:  5  9 10 13 14  * 18 19 20 23 24 25
%   16: 11 12 13  * 17 21
%   17: 11 12 13 16  * 18 21 22 23
%   18: 13 14 15 17  * 19 21 22 23
%   19: 13 14 15 18  * 20 23 24 25
%   20: 15 19  * 23 24 25
%   21: 11 12 13 16 17 18  * 22 23
%   22: 13 17 18 21  * 23
%   23: 13 14 15 17 18 19 20 21 22  * 24 25
%   24: 15 19 20 23  * 25
%   25: 15 19 20 23 24  *    
%
%    Below, we list the number of adjancencies to lower-indexed nodes, to 
%    the node itself, to higher-indexed nodes, the total number of 
%    adjacencies for this node, and the location of the first and last 
%    entries required to list this set of adjacencies in a single list 
%    of all the adjacencies.
%
%    N   Below  Self   Above   Total First  Last
%
%   --      --    --      --      --   ---     0
%    1:      0     1       5       6     1     6
%    2:      1     1       4       6     7    12
%    3:      2     1       9      12    13    24
%    4:      1     1       4       6    25    30
%    5:      2     1       6       9    31    39
%    6:      3     1       2       6    40    45
%    7:      4     1       4       9    46    54
%    8:      4     1       4       9    55    63
%    9:      4     1       4       9    62    72
%   10:      2     1       3       6    73    78
%   11:      6     1       5      12    79    90
%   12:      4     1       4       9    91    99
%   13:      9     1       9      19   100   118
%   14:      4     1       4       9   119   127
%   15:      5     1       6      12   128   139
%   16:      3     1       2       6   140   145
%   17:      4     1       4       9   146   154
%   18:      4     1       4       9   155   163
%   19:      4     1       4       9   164   172
%   20:      2     1       3       6   173   178
%   21:      6     1       2       9   179   187
%   22:      4     1       1       6   188   193
%   23:      9     1       2      12   194   205
%   24:      4     1       1       6   206   211
%   25:      5     1       0       6   212   217
%   --      --    --      --      --   218   ---
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    24 August 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters
%
%    Input, integer NODE_NUM, the number of nodes.
%
%    Input, integer TRI_NUM, the number of triangles.
%
%    Input, integer TRIANGLE_NODE(6,TRI_NUM), lists the nodes that
%    make up each triangle.  The first three nodes are the vertices,
%    in counterclockwise order.  The fourth value is the midside
%    node between nodes 1 and 2; the fifth and sixth values are
%    the other midside nodes in the logical order.
%
%    Input, integer TRIANGLE_NEIGHBOR(3,TRI_NUM), for each side of
%    a triangle, lists the neighboring triangle, or -1 if there is
%    no neighbor.
%
%    Output, integer ADJ_NUM, the number of adjacencies.
%
%    Output, integer ADJ_COL(NODE_NUM+1).  Information about column J is stored
%    in entries ADJ_COL(J) through ADJ_COL(J+1)-1 of ADJ.
%
  triangle_order = 6;
  adj_num = 0;
%
%  Set every node to be adjacent to itself.
%
  adj_col(1:node_num) = 1;
%
%  Examine each triangle.
%
  for triangle = 1 : tri_num

    n1 = triangle_node(1,triangle);
    n2 = triangle_node(2,triangle);
    n3 = triangle_node(3,triangle);
    n4 = triangle_node(4,triangle);
    n5 = triangle_node(5,triangle);
    n6 = triangle_node(6,triangle);
%
%  For sure, we add the adjacencies:
%    43 / (34)
%    51 / (15)
%    54 / (45)
%    62 / (26)
%    64 / (46)
%    65 / (56)
%
    adj_col(n3) = adj_col(n3) + 1;
    adj_col(n4) = adj_col(n4) + 1;
    adj_col(n1) = adj_col(n1) + 1;
    adj_col(n5) = adj_col(n5) + 1;
    adj_col(n4) = adj_col(n4) + 1;
    adj_col(n5) = adj_col(n5) + 1;
    adj_col(n2) = adj_col(n2) + 1;
    adj_col(n6) = adj_col(n6) + 1;
    adj_col(n4) = adj_col(n4) + 1;
    adj_col(n6) = adj_col(n6) + 1;
    adj_col(n5) = adj_col(n5) + 1;
    adj_col(n6) = adj_col(n6) + 1;
%
%  Add edges (1,2), (1,4), (2,4) if this is the first occurrence,
%  that is, if the edge (1,4,2) is on a boundary (TRIANGLE2 <= 0)
%  or if this triangle is the first of the pair in which the edge
%  occurs (TRIANGLE < TRIANGLE2).
%
%  Maybe add
%    21 / 12
%    41 / 14
%    42 / 24
%
    triangle2 = triangle_neighbor(1,triangle);

    if ( triangle2 < 0 | triangle < triangle2 )
      adj_col(n1) = adj_col(n1) + 1;
      adj_col(n2) = adj_col(n2) + 1;
      adj_col(n1) = adj_col(n1) + 1;
      adj_col(n4) = adj_col(n4) + 1;
      adj_col(n2) = adj_col(n2) + 1;
      adj_col(n4) = adj_col(n4) + 1;
    end
%
%  Maybe add
%    32 / 23
%    52 / 25
%    53 / 35
%
    triangle2 = triangle_neighbor(2,triangle);

    if ( triangle2 < 0 | triangle < triangle2 )
      adj_col(n2) = adj_col(n2) + 1;
      adj_col(n3) = adj_col(n3) + 1;
      adj_col(n2) = adj_col(n2) + 1;
      adj_col(n5) = adj_col(n5) + 1;
      adj_col(n3) = adj_col(n3) + 1;
      adj_col(n5) = adj_col(n5) + 1;
    end
%
%  Maybe add
%    31 / 13
%    61 / 16
%    63 / 36
%
    triangle2 = triangle_neighbor(3,triangle);

    if ( triangle2 < 0 | triangle < triangle2 )
      adj_col(n1) = adj_col(n1) + 1;
      adj_col(n3) = adj_col(n3) + 1;
      adj_col(n1) = adj_col(n1) + 1;
      adj_col(n6) = adj_col(n6) + 1;
      adj_col(n3) = adj_col(n3) + 1;
      adj_col(n6) = adj_col(n6) + 1;
    end
      
  end
%
%  We used ADJ_COL to count the number of entries in each column.
%  Convert it to pointers into the ADJ array.
%
  adj_col(2:node_num+1) = adj_col(1:node_num);

  adj_col(1) = 1;
  for i = 2 : node_num+1
    adj_col(i) = adj_col(i-1) + adj_col(i);
  end

  adj_num = adj_col(node_num+1) - 1;

  return
end
