# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <fstream>
# include <cmath>
# include <ctime>

using namespace std;

int main ( int argc, char *argv[] );
char ch_cap ( char c );
bool ch_eqi ( char c1, char c2 );
int ch_to_digit ( char c );
int diaedg ( double x0, double y0, double x1, double y1, double x2, double y2, 
  double x3, double y3 );
double *dtable_data_read ( char *input_file_name, int m, int n );
void dtable_header_read ( char *input_file_name, int *m, int *n );
int dtris2 ( int point_num, double point_xy[], int *tri_num, 
  int tri_vert[], int tri_nabe[] );
int file_column_count ( char *input_file_name );
void file_name_ext_get ( char *file_name, int *i, int *j );
char *file_name_ext_swap ( char *file_name, char *ext );
int file_row_count ( char *input_file_name );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
int i4_modp ( int i, int j );
int i4_sign ( int i );
int i4_wrap ( int ival, int ilo, int ihi );
void i4mat_transpose_print_some ( int m, int n, int a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
int *i4vec_indicator ( int n );
int *i4vec_sort_heap_index_a ( int n, int a[] );
void itable_data_write ( ofstream &output, int m, int n, int table[] );
void itable_header_write ( char *output_file_name, ofstream &output, 
  int m, int n );
void itable_triangulation_write ( char *input_file_name, char *output_file_name, 
  int m1, int n1, int m2, int n2, int table[] );
int lrline ( double xu, double yu, double xv1, double yv1, double xv2, 
  double yv2, double dv );
void perm_inv ( int n, int p[] );
double r8_epsilon ( void );
double r8_huge ( void );
double r8_max ( double x, double y );
double r8_min ( double x, double y );
void r82vec_permute ( int n, double a[], int p[] );
int *r82vec_sort_heap_index_a ( int n, double a[] );
void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
void s_blank_delete ( char *s );
int s_index_last_c ( char *s, char c );
int s_len_trim ( char *s );
double s_to_r8 ( char *s, int *lchar, bool *error );
bool s_to_r8vec ( char *s, int n, double rvec[] );
int s_word_count ( char *s );
int swapec ( int i, int *top, int *btri, int *bedg, int point_num, 
  double point_xy[], int tri_num, int tri_vert[], int tri_nabe[], 
  int stack[] );
void timestamp ( void );
char *timestring ( void );
void triangulation_order3_plot_eps ( char *file_name, int node_num, 
  double node_xy[], int triangle_num, int triangle_node[], int node_show, 
  int triangle_show );
void vbedg ( double x, double y, int point_num, double point_xy[], int tri_num, 
  int tri_vert[], int tri_nabe[], int *ltri, int *ledg, int *rtri, int *redg );

//****************************************************************************80

int main ( int argc, char *argv[] )

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for TABLE_DELAUNAY.
//
//  Discussion:
//
//    TABLE_DELAUNAY computes the Delaunay triangulation of a TABLE dataset.
//
//    The dataset is simply a set of points in the plane.
//
//    Thus, given a set of points V1, V2, ..., VN, we apply a standard 
//    Delaunay triangulation.  The Delaunay triangulation is an organization 
//    of the data into triples, forming a triangulation of the data, with
//    the property that the circumcircle of each triangle never contains
//    another data point.  
//
//  Modified:
//
//    22 June 2006
//
//  Author:
//
//    John Burkardt
//
//  Usage:
//
//    table_delaunay input_file_name
//
{ 
  int i;
  char *eps_file_name;
  char input_file_name[255];
  int m1;
  int m2;
  int node_num;
  bool node_show;
  char *output_file_name;
  double *table;
  int *triangle_neighbor;
  int *triangle_node;
  int triangle_num;
  bool triangle_show;

  cout << "\n";
  timestamp ( );

  cout << "\n";
  cout << "TABLE_DELAUNAY\n";
  cout << "  C++ version:\n";
  cout << "\n";
  cout << "  Compiled on " << __DATE__ << " at " << __TIME__ << ".\n";
  cout << "\n";
  cout << "  Read a TABLE dataset of N points in 2 dimensions,\n";
  cout << "  Compute the Delaunay triangulation.\n";
  cout << "  Write an integer TABLE dataset of the triangulation.\n";
//
//  If the input file was not specified, get it now.
//
  if ( argc <= 1 ) 
  {
    cout << "\n";
    cout << "TABLE_DELAUNAY:\n";
    cout << "  Please enter the name of the input file.\n";

    cin.getline ( input_file_name, sizeof ( input_file_name ) );
  }
  else 
  {
    strcpy ( input_file_name, argv[1] );
  } 

  output_file_name = file_name_ext_swap ( input_file_name, "delaunay.txt" );
//
//  Read the point coordinates.
//
  dtable_header_read ( input_file_name, &m1, &node_num );

  cout << "\n";
  cout << "  Read the header of \"" << input_file_name << "\"\n";
  cout << "\n";
  cout << "  The spatial dimension of the data = " << m1 << "\n";
  cout << "  The number of points N = " << node_num << "\n";

  if ( m1 != 2 )
  {
    cout << "\n";
    cout << "HANDLE - Fatal error!\n";
    cout << "  The input spatial dimension is not 2.\n";
    exit ( 1 );
  }

  table = dtable_data_read ( input_file_name, m1, node_num );

  cout << "\n";
  cout << "  Read the data of \"" << input_file_name << "\"\n";

  r8mat_transpose_print_some ( m1, node_num, table, 1, 1, 5, 5, 
    "  5 by 5 portion of node data read from file:" );
//
//  Determine the Delaunay triangulation.
//
  m2 = 3;

  triangle_node = new int[m2*3*node_num];
  triangle_neighbor = new int[m2*3*node_num];

  dtris2 ( node_num, table, &triangle_num, triangle_node, triangle_neighbor );
//
//  Print a portion of the triangulation.
//
  cout << "\n";
  cout << "  Computed the triangulation.\n";
  cout << "  Number of triangles is " << triangle_num << "\n";

  i4mat_transpose_print_some ( m2, triangle_num, triangle_node, 
    1, 1, 3, 5, "  3 by 5 portion of triangulation data:" );
//
//  Write the triangulation to a file.
//
  itable_triangulation_write ( input_file_name, output_file_name, 
    m1, node_num, m2, triangle_num, triangle_node );

  cout << "\n";
  cout << "  Wrote the triangulation data to \""
       << output_file_name << "\".\n";
//
//  Plot the triangulation.
//
  eps_file_name = file_name_ext_swap ( input_file_name, "delaunay.eps" );

  node_show = true;
  triangle_show = true;

  triangulation_order3_plot_eps ( eps_file_name, node_num, table, 
    triangle_num, triangle_node, node_show, triangle_show );

  cout << "\n";
  cout << "  Draw a picture of the triangulation data in \""
       << eps_file_name << "\".\n";
//
//  Terminate execution.
//
  cout << "\n";
  cout << "TABLE_DELAUNAY:\n";
  cout << "  Normal end of execution.\n";

  cout << "\n";
  timestamp ( );

  delete [] table;
  delete [] triangle_node;
  delete [] triangle_neighbor;

  return 0;
}
//****************************************************************************80

char ch_cap ( char c )

//****************************************************************************80
//
//  Purpose:
//
//    CH_CAP capitalizes a single character.
//
//  Discussion:
//
//    This routine should be equivalent to the library "toupper" function.
//
//  Modified:
//
//    19 July 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char C, the character to capitalize.
//
//    Output, char CH_CAP, the capitalized character.
//
{
  if ( 97 <= c && c <= 122 ) 
  {
    c = c - 32;
  }   

  return c;
}
//****************************************************************************80*

bool ch_eqi ( char c1, char c2 )

//****************************************************************************80*
//
//  Purpose:
//
//    CH_EQI is true if two characters are equal, disregarding case.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char C1, char C2, the characters to compare.
//
//    Output, bool CH_EQI, is true if the two characters are equal,
//    disregarding case.
//
{
  if ( 97 <= c1 && c1 <= 122 ) 
  {
    c1 = c1 - 32;
  } 
  if ( 97 <= c2 && c2 <= 122 ) 
  {
    c2 = c2 - 32;
  }     

  return ( c1 == c2 );
}
//****************************************************************************80

int ch_to_digit ( char c )

//****************************************************************************80
//
//  Purpose:
//
//    CH_TO_DIGIT returns the integer value of a base 10 digit.
//
//  Example:
//
//     C   DIGIT
//    ---  -----
//    '0'    0
//    '1'    1
//    ...  ...
//    '9'    9
//    ' '    0
//    'X'   -1
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char C, the decimal digit, '0' through '9' or blank are legal.
//
//    Output, int CH_TO_DIGIT, the corresponding integer value.  If C was
//    'illegal', then DIGIT is -1.
//
{
  int digit;

  if ( '0' <= c && c <= '9' )
  {
    digit = c - '0';
  }
  else if ( c == ' ' )
  {
    digit = 0;
  }
  else
  {
    digit = -1;
  }

  return digit;
}
//****************************************************************************80

int diaedg ( double x0, double y0, double x1, double y1, double x2, double y2, 
  double x3, double y3 )

//****************************************************************************80
//
//  Purpose:
//
//    DIAEDG chooses a diagonal edge.
//
//  Discussion:
//
//    The routine determines whether 0--2 or 1--3 is the diagonal edge
//    that should be chosen, based on the circumcircle criterion, where
//    (X0,Y0), (X1,Y1), (X2,Y2), (X3,Y3) are the vertices of a simple
//    quadrilateral in counterclockwise order.
//
//  Modified:
//
//    28 August 2003
//
//  Author:
//
//    Barry Joe,
//    Department of Computing Science,
//    University of Alberta,
//    Edmonton, Alberta, Canada  T6G 2H1
//
//  Reference:
//
//    Barry Joe,
//    GEOMPACK - a software package for the generation of meshes
//    using geometric algorithms,
//    Advances in Engineering Software,
//    Volume 13, pages 325-331, 1991.
//
//  Parameters:
//
//    Input, double X0, Y0, X1, Y1, X2, Y2, X3, Y3, the coordinates of the 
//    vertices of a quadrilateral, given in counter clockwise order.
//
//    Output, int DIAEDG, chooses a diagonal:
//    +1, if diagonal edge 02 is chosen;
//    -1, if diagonal edge 13 is chosen;
//     0, if the four vertices are cocircular.
//
{
  double ca;
  double cb;
  double dx10;
  double dx12;
  double dx30;
  double dx32;
  double dy10;
  double dy12;
  double dy30;
  double dy32;
  double s;
  double tol;
  double tola;
  double tolb;
  int value;

  tol = 100.0 * r8_epsilon ( );

  dx10 = x1 - x0;
  dy10 = y1 - y0;
  dx12 = x1 - x2;
  dy12 = y1 - y2;
  dx30 = x3 - x0;
  dy30 = y3 - y0;
  dx32 = x3 - x2;
  dy32 = y3 - y2;

  tola = tol * r8_max ( fabs ( dx10 ), 
               r8_max ( fabs ( dy10 ), 
               r8_max ( fabs ( dx30 ), fabs ( dy30 ) ) ) );

  tolb = tol * r8_max ( fabs ( dx12 ), 
               r8_max ( fabs ( dy12 ), 
               r8_max ( fabs ( dx32 ), fabs ( dy32 ) ) ) );

  ca = dx10 * dx30 + dy10 * dy30;
  cb = dx12 * dx32 + dy12 * dy32;

  if ( tola < ca && tolb < cb )
  {
    value = -1;
  }
  else if ( ca < -tola && cb < -tolb )
  {
    value = 1;
  }
  else
  {
    tola = r8_max ( tola, tolb );
    s = ( dx10 * dy30 - dx30 * dy10 ) * cb 
      + ( dx32 * dy12 - dx12 * dy32 ) * ca;

    if ( tola < s )
    {
      value = -1;
    }
    else if ( s < -tola )
    {
      value = 1;
    }
    else
    {
      value = 0;
    }

  }

  return value;
}
//****************************************************************************80

double *dtable_data_read ( char *input_file_name, int m, int n )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_DATA_READ reads the data from a real TABLE file.
//
//  Discussion:
//
//    The file is assumed to contain one record per line.
//
//    Records beginning with the '#' character are comments, and are ignored.
//    Blank lines are also ignored.
//
//    Each line that is not ignored is assumed to contain exactly (or at least)
//    M real numbers, representing the coordinates of a point.
//
//    There are assumed to be exactly (or at least) N such records.
//
//  Modified:
//
//    27 January 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILE_NAME, the name of the input file.
//
//    Input, int M, the number of spatial dimensions.
//
//    Input, int N, the number of points.  The program
//    will stop reading data once N values have been read.
//
//    Output, double DTABLE_DATA_READ[M*N], the table data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  char line[255];
  double *table;
  double *x;

  input.open ( input_file_name );

  if ( !input )
  {
    cout << "\n";
    cout << "DTABLE_DATA_READ - Fatal error!\n";
    cout << "  Could not open the input file: \"" << input_file_name << "\"\n";
    return NULL;
  }

  table = new double[m*n];

  x = new double[m];

  j = 0;

  while ( j < n )
  {
    input.getline ( line, sizeof ( line ) );

    if ( input.eof ( ) )
    {
      break;
    }

    if ( line[0] == '#' || s_len_trim ( line ) == 0 )
    {
      continue;
    }

    error = s_to_r8vec ( line, m, x );

    if ( error )
    {
      continue;
    }

    for ( i = 0; i < m; i++ )
    {
      table[i+j*m] = x[i];
    }
    j = j + 1;

  }

  input.close ( );

  delete [] x;

  return table;
}
//****************************************************************************80
 
void dtable_header_read ( char *input_file_name, int *m, int *n )
 
//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_HEADER_READ reads the header from a real TABLE file.
//
//  Modified:
//
//    04 June 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILE_NAME, the name of the input file.
//
//    Output, int *M, the number of spatial dimensions.
//
//    Output, int *N, the number of points.
//
{
  *m = file_column_count ( input_file_name );

  if ( *m <= 0 )
  {
    cout << "\n";
    cout << "DTABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_COLUMN_COUNT failed.\n";
    *n = -1;
    return;
  }

  *n = file_row_count ( input_file_name );

  if ( *n <= 0 )
  {
    cout << "\n";
    cout << "DTABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_ROW_COUNT failed.\n";
    return;
  }

  return;
}
//****************************************************************************80

int dtris2 ( int point_num, double point_xy[], int *tri_num, 
  int tri_vert[], int tri_nabe[] )

//****************************************************************************80
//
//  Purpose:
//
//    DTRIS2 constructs a Delaunay triangulation of 2D vertices.
//
//  Discussion:
//
//    The routine constructs the Delaunay triangulation of a set of 2D vertices
//    using an incremental approach and diagonal edge swaps.  Vertices are
//    first sorted in lexicographically increasing (X,Y) order, and
//    then are inserted one at a time from outside the convex hull.
//
//  Modified:
//
//    15 January 2004
//
//  Author:
//
//    Barry Joe,
//    Department of Computing Science,
//    University of Alberta,
//    Edmonton, Alberta, Canada  T6G 2H1
//
//  Reference:
//
//    Barry Joe,
//    GEOMPACK - a software package for the generation of meshes
//    using geometric algorithms,
//    Advances in Engineering Software,
//    Volume 13, pages 325-331, 1991.
//
//  Parameters:
//
//    Input, int POINT_NUM, the number of vertices.
//
//    Input/output, double POINT_XY[POINT_NUM*2], the coordinates of the vertices.
//    On output, the vertices have been sorted into dictionary order.
//
//    Output, int *TRI_NUM, the number of triangles in the triangulation;
//    TRI_NUM is equal to 2*POINT_NUM - NB - 2, where NB is the number
//    of boundary vertices.
//
//    Output, int TRI_VERT[TRI_NUM*3], the nodes that make up each triangle.
//    The elements are indices of POINT_XY.  The vertices of the triangles are
//    in counter clockwise order.
//
//    Output, int TRI_NABE[TRI_NUM*3], the triangle neighbor list.
//    Positive elements are indices of TIL; negative elements are used for links
//    of a counter clockwise linked list of boundary edges; LINK = -(3*I + J-1)
//    where I, J = triangle, edge index; TRI_NABE[I,J] refers to
//    the neighbor along edge from vertex J to J+1 (mod 3).
//
//    Output, int DTRIS2, is 0 for no error.
{
  double cmax;
  int e;
  int error;
  int i;
  int *indx;
  int j;
  int k;
  int l;
  int ledg;
  int lr;
  int ltri;
  int m;
  int m1;
  int m2;
  int n;
  int redg;
  int rtri;
  int *stack;
  int t;
  double tol;
  int top;

  stack = new int[point_num];

  tol = 100.0 * r8_epsilon ( );
//
//  Sort the vertices by increasing (x,y).
//
  indx = r82vec_sort_heap_index_a ( point_num, point_xy );

  r82vec_permute ( point_num, point_xy, indx );
//
//  Make sure that the data points are "reasonably" distinct.
//
  m1 = 1;

  for ( i = 2; i <= point_num; i++ )
  {
    m = m1;
    m1 = i;

    k = -1;

    for ( j = 0; j <= 1; j++ )
    {
      cmax = r8_max ( fabs ( point_xy[2*(m-1)+j] ), 
                     fabs ( point_xy[2*(m1-1)+j] ) );

      if ( tol * ( cmax + 1.0 ) 
           < fabs ( point_xy[2*(m-1)+j] - point_xy[2*(m1-1)+j] ) ) 
      {
        k = j;
        break;
      }

    }

    if ( k == -1 )
    {
      cout << "\n";
      cout << "DTRIS2 - Fatal error!\n";
      cout << "  Fails for point number I = " << i << "\n";
      cout << "  M =  " << m  << "\n";
      cout << "  M1 = " << m1 << "\n";
      cout << "  X,Y(M)  = " << point_xy[2*(m-1)+0] << "  "
                             << point_xy[2*(m-1)+1] << "\n";
      cout << "  X,Y(M1) = " << point_xy[2*(m1-1)+0] << "  "
                             << point_xy[2*(m1-1)+1] << "\n";
      delete [] stack;
      return 224;
    }

  }
//
//  Starting from points M1 and M2, search for a third point M that
//  makes a "healthy" triangle (M1,M2,M)
//
  m1 = 1;
  m2 = 2;
  j = 3;

  for ( ; ; )
  {
    if ( point_num < j )
    {
      cout << "\n";
      cout << "DTRIS2 - Fatal error!\n";
      delete [] stack;
      return 225;
    }

    m = j;

    lr = lrline ( point_xy[2*(m-1)+0], point_xy[2*(m-1)+1],
      point_xy[2*(m1-1)+0], point_xy[2*(m1-1)+1], 
      point_xy[2*(m2-1)+0], point_xy[2*(m2-1)+1], 0.0 );

    if ( lr != 0 )
    {
      break;
    }

    j = j + 1;

  }
//
//  Set up the triangle information for (M1,M2,M), and for any other
//  triangles you created because points were collinear with M1, M2.
//
  *tri_num = j - 2;

  if ( lr == -1 )
  {
    tri_vert[3*0+0] = m1;
    tri_vert[3*0+1] = m2;
    tri_vert[3*0+2] = m;
    tri_nabe[3*0+2] = -3;

    for ( i = 2; i <= *tri_num; i++ )
    {
      m1 = m2;
      m2 = i+1;
      tri_vert[3*(i-1)+0] = m1;
      tri_vert[3*(i-1)+1] = m2;
      tri_vert[3*(i-1)+2] = m;
      tri_nabe[3*(i-1)+0] = -3 * i;
      tri_nabe[3*(i-1)+1] = i;
      tri_nabe[3*(i-1)+2] = i - 1;

    }

    tri_nabe[3*(*tri_num-1)+0] = -3 * (*tri_num) - 1;
    tri_nabe[3*(*tri_num-1)+1] = -5;
    ledg = 2;
    ltri = *tri_num;
  }
  else
  {
    tri_vert[3*0+0] = m2;
    tri_vert[3*0+1] = m1;
    tri_vert[3*0+2] = m;
    tri_nabe[3*0+0] = -4;

    for ( i = 2; i <= *tri_num; i++ )
    {
      m1 = m2;
      m2 = i+1;
      tri_vert[3*(i-1)+0] = m2;
      tri_vert[3*(i-1)+1] = m1;
      tri_vert[3*(i-1)+2] = m;
      tri_nabe[3*(i-2)+2] = i;
      tri_nabe[3*(i-1)+0] = -3 * i - 3;
      tri_nabe[3*(i-1)+1] = i - 1;
    }

    tri_nabe[3*(*tri_num-1)+2] = -3 * (*tri_num);
    tri_nabe[3*0+1] = -3 * (*tri_num) - 2;
    ledg = 2;
    ltri = 1;
  }
//
//  Insert the vertices one at a time from outside the convex hull,
//  determine visible boundary edges, and apply diagonal edge swaps until
//  Delaunay triangulation of vertices (so far) is obtained.
//
  top = 0;

  for ( i = j+1; i <= point_num; i++ )
  {
    m = i;
    m1 = tri_vert[3*(ltri-1)+ledg-1];

    if ( ledg <= 2 )
    {
      m2 = tri_vert[3*(ltri-1)+ledg];
    }
    else
    {
      m2 = tri_vert[3*(ltri-1)+0];
    }

    lr = lrline ( point_xy[2*(m-1)+0], point_xy[2*(m-1)+1], 
      point_xy[2*(m1-1)+0], point_xy[2*(m1-1)+1], 
      point_xy[2*(m2-1)+0], point_xy[2*(m2-1)+1], 0.0 );

    if ( 0 < lr )
    {
      rtri = ltri;
      redg = ledg;
      ltri = 0;
    }
    else
    {
      l = -tri_nabe[3*(ltri-1)+ledg-1];
      rtri = l / 3;
      redg = (l % 3) + 1;
    }

    vbedg ( point_xy[2*(m-1)+0], point_xy[2*(m-1)+1], point_num, 
      point_xy, *tri_num, tri_vert, tri_nabe, &ltri, &ledg, &rtri, &redg );

    n = *tri_num + 1;
    l = -tri_nabe[3*(ltri-1)+ledg-1];

    for ( ; ; )
    {
      t = l / 3;
      e = ( l % 3 ) + 1;
      l = -tri_nabe[3*(t-1)+e-1];
      m2 = tri_vert[3*(t-1)+e-1];

      if ( e <= 2 )
      {
        m1 = tri_vert[3*(t-1)+e];
      }
      else
      {
        m1 = tri_vert[3*(t-1)+0];
      }

      *tri_num = *tri_num + 1;
      tri_nabe[3*(t-1)+e-1] = *tri_num;
      tri_vert[3*(*tri_num-1)+0] = m1;
      tri_vert[3*(*tri_num-1)+1] = m2;
      tri_vert[3*(*tri_num-1)+2] = m;
      tri_nabe[3*(*tri_num-1)+0] = t;
      tri_nabe[3*(*tri_num-1)+1] = *tri_num - 1;
      tri_nabe[3*(*tri_num-1)+2] = *tri_num + 1;
      top = top + 1;

      if ( point_num < top )
      {
        cout << "\n";
        cout << "DTRIS2 - Fatal error!\n";
        cout << "  Stack overflow.\n";
        delete [] stack;
        return 8;
      }

      stack[top-1] = *tri_num;

      if ( t == rtri && e == redg )
      {
        break;
      }

    }

    tri_nabe[3*(ltri-1)+ledg-1] = -3 * n - 1;
    tri_nabe[3*(n-1)+1] = -3 * (*tri_num) - 2;
    tri_nabe[3*(*tri_num-1)+2] = -l;
    ltri = n;
    ledg = 2;

    error = swapec ( m, &top, &ltri, &ledg, point_num, point_xy, *tri_num, 
      tri_vert, tri_nabe, stack );

    if ( error != 0 )
    {
      cout << "\n";
      cout << "DTRIS2 - Fatal error!\n";
      cout << "  Error return from SWAPEC.\n";
      delete [] stack;
      return error;
    }

  }
//
//  Now account for the sorting that we did.
//
  for ( i = 0; i < 3; i++ )
  {
    for ( j = 0; j < *tri_num; j++ )
    {
      tri_vert[i+j*3] = indx [ tri_vert[i+j*3] - 1 ];
    }
  }

  perm_inv ( point_num, indx );

  r82vec_permute ( point_num, point_xy, indx );

  delete [] indx;
  delete [] stack;

  return 0;
}
//****************************************************************************80

int file_column_count ( char *input_file_name )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
//
//  Discussion:
//
//    The file is assumed to be a simple text file.
//
//    Most lines of the file is presumed to consist of COLUMN_NUM words, separated
//    by spaces.  There may also be some blank lines, and some comment lines,
//    which have a "#" in column 1.
//
//    The routine tries to find the first non-comment non-blank line and
//    counts the number of words in that line.
//
//    If all lines are blanks or comments, it goes back and tries to analyze
//    a comment line.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILE_NAME, the name of the file.
//
//    Output, int FILE_COLUMN_COUNT, the number of columns assumed 
//    to be in the file.
//
{
  int column_num;
  ifstream input;
  bool got_one;
  char line[256];
//
//  Open the file.
//
  input.open ( input_file_name );

  if ( !input )
  {
    column_num = -1;
    cout << "\n";
    cout << "FILE_COLUMN_COUNT - Fatal error!\n";
    cout << "  Could not open the file:\n";
    cout << "  \"" << input_file_name << "\"\n";
    return column_num;
  }
//
//  Read one line, but skip blank lines and comment lines.
//
  got_one = false;

  for ( ; ; )
  {
    input.getline ( line, sizeof ( line ) );

    if ( input.eof ( ) )
    {
      break;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      continue;
    }

    if ( line[0] == '#' )
    {
      continue;
    }

    got_one = true;
    break;

  }

  if ( !got_one )
  {
    input.close ( );

    input.open ( input_file_name );

    for ( ; ; )
    {
      input.getline ( line, sizeof ( line ) );

      if ( input.eof ( ) )
      {
        break;
      }

      if ( s_len_trim ( line ) == 0 )
      {
        continue;
      }

      got_one = true;
      break;

    }

  }

  input.close ( );

  if ( !got_one )
  {
    cout << "\n";
    cout << "FILE_COLUMN_COUNT - Warning!\n";
    cout << "  The file does not seem to contain any data.\n";
    return -1;
  }

  column_num = s_word_count ( line );

  return column_num;
}
//****************************************************************************80

void file_name_ext_get ( char *file_name, int *i, int *j )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_NAME_EXT_GET determines the "extension" of a file name.
//
//  Definition:
//
//    The "extension" of a file name is the string of characters
//    that appears after the LAST period in the name.  A file
//    with no period, or with a period as the last character
//    in the name, has a "null" extension.
//
//  Note:
//
//    Blanks are unusual in file names.  This routine ignores all
//    trailing blanks, but will treat initial or internal blanks
//    as regular characters acceptable in a file name.
//
//  Examples:
//
//    FILE_NAME   I  J
//
//    bob.for     3  6
//    N.B.C.D     5  6
//    Naomi.      5  5
//    Arthur     -1 -1
//    .com        0  0
//
//  Modified:
//
//    17 July 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *FILE_NAME, a file name to be examined.
//
//    Output, int *I, *J, the indices of the first and last characters
//    in the file extension.
//
//    If no period occurs in FILE_NAME, then
//      I = J = -1;
//    Otherwise,
//      I is the position of the LAST period in FILE_NAME, and J is the
//      position of the last nonblank character following the period.
//
{
  *i = s_index_last_c ( file_name, '.' );

  if ( *i == -1 )
  {
    *j = -1;
  }
  else
  {
    *j = s_len_trim ( file_name ) - 1;
  }

  return;
}
//****************************************************************************80

char *file_name_ext_swap ( char *file_name, char *ext )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
//
//  Discussion:
//
//    NO THANKS: The creation of this routine was made more difficult by the clumsy
//    construction and misleading documentation of the C library routines STRNCAT
//    and STRCAT, which I was planning to use.
//
//  Definition:
//
//    The "extension" of a file name is the string of characters
//    that appears after the LAST period in the name.  A file
//    with no period, or with a period as the last character
//    in the name, has a "null" extension.
//
//  Examples:
//
//          Input           Output
//    ================     ==================
//    FILE_NAME    EXT     FILE_NAME_EXT_SWAP
//
//    bob.for      obj     bob.obj
//    bob.bob.bob  txt     bob.bob.txt
//    bob          yak     bob.yak
//
//  Modified:
//
//    06 December 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *FILE_NAME, a file name.
//
//    Input, char *EXT, the extension to be used on the output
//    copy of FILE_NAME, replacing the current extension if any.
//
//    Output, char *FILE_NAME_EXT_SWAP, the file name with the new extension.
//
{
  int ext_len;
  int file_name_len;
  char *file_name2;
  int i;
  int j;
  int period;
  char *s;
  char *t;
//
  ext_len = s_len_trim ( ext );
  file_name_len = s_len_trim ( file_name );
//
//  Call FILE_NAME_EXT_GET to get I, the index of the period character
//  beginning the file extension.
//
  file_name_ext_get ( file_name, &period, &j );
//
//  If there is no extension, point to where the "." should be.
//
  if ( period == -1 )
  {
    period = file_name_len;
  }

  file_name2 = new char[ period + 1 + ext_len + 1];

  s = file_name2;
  t = file_name;
  for ( i = 0; i < period; i++ )
  {
    *s = *t;
    s++;
    t++;
  }
  *s = '.';
  s++;

  t = ext;
  for ( i = 0; i < ext_len; i++ )
  {
    *s = *t;
    s++;
    t++;
  }

  *s = '\0';

  return file_name2;
}
//****************************************************************************80

int file_row_count ( char *input_file_name )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_ROW_COUNT counts the number of row records in a file.
//
//  Discussion:
//
//    It does not count lines that are blank, or that begin with a
//    comment symbol '#'.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILE_NAME, the name of the input file.
//
//    Output, int FILE_ROW_COUNT, the number of rows found.
//
{
  int bad_num;
  int comment_num;
  ifstream input;
  int i;
  char line[100];
  int record_num;
  int row_num;

  row_num = 0;
  comment_num = 0;
  record_num = 0;
  bad_num = 0;

  input.open ( input_file_name );

  if ( !input )
  {
    cout << "\n";
    cout << "FILE_ROW_COUNT - Fatal error!\n";
    cout << "  Could not open the input file: \"" << input_file_name << "\"\n";
    return (-1);
  }

  for ( ; ; )
  {
    input.getline ( line, sizeof ( line ) );

    if ( input.eof ( ) )
    {
      break;
    }

    record_num = record_num + 1;

    if ( line[0] == '#' )
    {
      comment_num = comment_num + 1;
      continue;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      comment_num = comment_num + 1;
      continue;
    }

    row_num = row_num + 1;

  }

  input.close ( );

  return row_num;
}
//****************************************************************************80

int i4_max ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MAX returns the maximum of two integers.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, are two integers to be compared.
//
//    Output, int I4_MAX, the larger of I1 and I2.
//
{
  if ( i2 < i1 )
  {
    return i1;
  }
  else
  {
    return i2;
  }

}
//****************************************************************************80

int i4_min ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MIN returns the smaller of two integers.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, two integers to be compared.
//
//    Output, int I4_MIN, the smaller of I1 and I2.
//
{
  if ( i1 < i2 )
  {
    return i1;
  }
  else
  {
    return i2;
  }

}
//****************************************************************************80

int i4_modp ( int i, int j )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MODP returns the nonnegative remainder of integer division.
//
//  Formula:
//
//    If 
//      NREM = I4_MODP ( I, J ) 
//      NMULT = ( I - NREM ) / J
//    then
//      I = J * NMULT + NREM
//    where NREM is always nonnegative.
//
//  Comments:
//
//    The MOD function computes a result with the same sign as the
//    quantity being divided.  Thus, suppose you had an angle A,
//    and you wanted to ensure that it was between 0 and 360.
//    Then mod(A,360) would do, if A was positive, but if A
//    was negative, your result would be between -360 and 0.
//
//    On the other hand, I4_MODP(A,360) is between 0 and 360, always.
//
//  Examples:
//
//        I         J     MOD  I4_MODP   I4_MODP Factorization
// 
//      107        50       7       7    107 =  2 *  50 + 7
//      107       -50       7       7    107 = -2 * -50 + 7
//     -107        50      -7      43   -107 = -3 *  50 + 43
//     -107       -50      -7      43   -107 =  3 * -50 + 43
//
//  Modified:
//
//    26 May 1999
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I, the number to be divided.
//
//    Input, int J, the number that divides I.
//
//    Output, int I4_MODP, the nonnegative remainder when I is 
//    divided by J.
//
{
  int value;

  if ( j == 0 )
  {
    cout << "\n";
    cout << "I4_MODP - Fatal error!\n";
    cout << "  I4_MODP ( I, J ) called with J = " << j << "\n";
    exit ( 1 );
  }

  value = i % j;

  if ( value < 0 )
  {
    value = value + abs ( j );
  }

  return value;
}
//****************************************************************************80

int i4_sign ( int i )

//****************************************************************************80
//
//  Purpose:
//
//    I4_SIGN returns the sign of an integer.
//
//  Discussion:
//
//    The sign of 0 and all positive integers is taken to be +1.
//    The sign of all negative integers is -1.
//
//  Modified:
//
//    06 May 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I, the integer whose sign is desired.
//
//    Output, int I4_SIGN, the sign of I.
{
  if ( i < 0 ) 
  {
    return (-1);
  }
  else
  {
    return 1;
  }

}
//****************************************************************************80*

int i4_wrap ( int ival, int ilo, int ihi )

//****************************************************************************80*
//
//  Purpose:
//
//    I4_WRAP forces an integer to lie between given limits by wrapping.
//
//  Example:
//
//    ILO = 4, IHI = 8
//
//    I  I4_WRAP
//
//    -2     8
//    -1     4
//     0     5
//     1     6
//     2     7
//     3     8
//     4     4
//     5     5
//     6     6
//     7     7
//     8     8
//     9     4
//    10     5
//    11     6
//    12     7
//    13     8
//    14     4
//
//  Modified:
//
//    19 August 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int IVAL, an integer value.
//
//    Input, int ILO, IHI, the desired bounds for the integer value.
//
//    Output, int I4_WRAP, a "wrapped" version of IVAL.
//
{
  int jhi;
  int jlo;
  int value;
  int wide;

  jlo = i4_min ( ilo, ihi );
  jhi = i4_max ( ilo, ihi );

  wide = jhi + 1 - jlo;

  if ( wide == 1 )
  {
    value = jlo;
  }
  else
  {
    value = jlo + i4_modp ( ival - jlo, wide );
  }

  return value;
}
//****************************************************************************80

void i4mat_transpose_print_some ( int m, int n, int a[], int ilo, int jlo, 
  int ihi, int jhi, char *title )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_TRANSPOSE_PRINT_SOME prints some of an integer matrix, transposed.
//
//  Modified:
//
//    09 February 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows of the matrix.
//    M must be positive.
//
//    Input, int N, the number of columns of the matrix.
//    N must be positive.
//
//    Input, int A[M*N], the matrix.
//
//    Input, int ILO, JLO, IHI, JHI, designate the first row and
//    column, and the last row and column to be printed.
//
//    Input, char *TITLE, a title for the matrix.
{
# define INCX 10

  int i;
  int i2hi;
  int i2lo;
  int j;
  int j2hi;
  int j2lo;

  if ( 0 < s_len_trim ( title ) )
  {
    cout << "\n";
    cout << title << "\n";
  }
//
//  Print the columns of the matrix, in strips of INCX.
//
  for ( i2lo = ilo; i2lo <= ihi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    i2hi = i4_min ( i2hi, m );
    i2hi = i4_min ( i2hi, ihi );

    cout << "\n";
//
//  For each row I in the current range...
//
//  Write the header.
//
    cout << "  Row:    ";
    for ( i = i2lo; i <= i2hi; i++ )
    {
      cout << setw(7) << i << "       ";
    }
    cout << "\n";
    cout << "  Col\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    j2lo = i4_max ( jlo, 1 );
    j2hi = i4_min ( jhi, n );

    for ( j = j2lo; j <= j2hi; j++ )
    {
//
//  Print out (up to INCX) entries in column J, that lie in the current strip.
//
      cout << setw(5) << j << "  ";
      for ( i = i2lo; i <= i2hi; i++ )
      {
        cout << setw(6) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }

  }

  cout << "\n";

  return;
# undef INCX
}
//****************************************************************************80

void itable_data_write ( ofstream &output, int m, int n, int table[] )

//****************************************************************************80
//
//  Purpose:
//
//    ITABLE_DATA_WRITE writes data to an integer TABLE file.
//
//  Modified:
//
//    11 December 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, ofstream &OUTPUT, a pointer to the output stream.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, int TABLE[M*N], the table data.
//
{
  int i;
  int j;
  char *s;

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << setw(10) << table[i+j*m] << "  ";
    }
    output << "\n";
  }

  output.close ( );

  return;
}
//****************************************************************************80
 
void itable_header_write ( char *output_file_name, ofstream &output, int m, 
  int n )
 
//****************************************************************************80
//
//  Purpose:
//
//    ITABLE_HEADER_WRITE writes the header of an integer TABLE file.
//
//  Modified:
//
//    22 March 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *OUTPUT_FILE_NAME, the output file name.
//
//    Input, ofstream &OUTPUT, the output stream.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
{
  char *s;
 
  s = timestring ( );
 
  output << "#  " << output_file_name << "\n";
  output << "#  created by itable_write in table_io.C" << "\n";
  output << "#  at " << s << "\n";
  output << "#\n";
  output << "#  Spatial dimension M = " << m << "\n";
  output << "#  Number of points N = " << n << "\n";
  output << "#\n";
 
  delete [] s;

  return;
}
//****************************************************************************80

void itable_triangulation_write ( char *input_file_name, char *output_file_name, 
  int m1, int n1, int m2, int n2, int table[] )

//****************************************************************************80
//
//  Purpose:
//
//    ITABLE_TRIANGULATION_WRITE writes an integer triangulation table to a file.
//
//  Modified:
//
//    22 June 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILE_NAME, the input file name.
//
//    Input, char *OUTPUT_FILE_NAME, the output file name.
//
//    Input, int M1, the spatial dimension of the nodes (should be 2).
//
//    Input, int N1, the number of nodes.
//
//    Input, int M2, the "spatial" dimension of the triangles (should be 3).
//
//    Input, int N, the number of triangles.
//
//    Input, int TABLE[M2*N2], the triangulation data.
//
{
  ofstream output;

  output.open ( output_file_name );

  if ( !output )
  {
    cout << "\n";
    cout << "ITABLE_TRIANGULATION_WRITE - Fatal error!\n";
    cout << "  Could not open the output file.\n";
    return;
  }

  itable_header_write ( output_file_name, output, m2, n2 );

  output << "#  Node data from \"" << input_file_name << "\"\n";
  output << "#  The node spatial dimension was " << m1 << "\n";
  output << "#  The number of nodes was " << n1 << "\n";
  output << "#\n";
  output << "#  The triangulation was computed by DTRIS2.\n";
  output << "#  The data was written to \"" << output_file_name << "\".\n";
  output << "#  by ITABLE_TRIANGULATION_WRITE.C.\n";
  output << "#\n";

  itable_data_write ( output, m2, n2, table );

  output.close ( );

  return;
}
//****************************************************************************80

int *i4vec_indicator ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_INDICATOR sets an integer vector to the indicator vector.
//
//  Modified:
//
//    13 January 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of elements of A.
//
//    Output, int I4VEC_INDICATOR(N), the initialized array.
//
{
  int *a;
  int i;

  a = new int[n];

  for ( i = 0; i < n; i++ )
  {
    a[i] = i + 1;
  }

  return a;
}
//****************************************************************************80

int *i4vec_sort_heap_index_a ( int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an integer vector.
//
//  Discussion:
//
//    The sorting is not actually carried out.  Rather an index array is
//    created which defines the sorting.  This array may be used to sort
//    or index the array, or to sort or index related arrays keyed on the
//    original array.
//
//    Once the index array is computed, the sorting can be carried out
//    "implicitly:
//
//      A(INDX(I)), I = 1 to N is sorted,
//
//    after which A(I), I = 1 to N is sorted.
//
//  Modified:
//
//    30 March 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input, int A[N], an array to be index-sorted.
//
//    Output, int I4VEC_SORT_HEAP_INDEX_A[N], contains the sort index.  The
//    I-th element of the sorted array is A(INDX(I)).
//
{
  int aval;
  int i;
  int *indx;
  int indxt;
  int ir;
  int j;
  int l;

  indx = new int[n];

  for ( i = 1; i <= n; i++ )
  {
    indx[i-1] = i;
  }

  l = n / 2 + 1;
  ir = n;

  for ( ; ; )
  {
    if ( 1 < l )
    {
      l = l - 1;
      indxt = indx[l-1];
      aval = a[indxt-1];
    }
    else
    {
      indxt = indx[ir-1];
      aval = a[indxt-1];
      indx[ir-1] = indx[0];
      ir = ir - 1;

      if ( ir == 1 )
      {
        indx[0] = indxt;
        return indx;
      }

    }

    i = l;
    j = l + l;

    while ( j <= ir )
    {
      if ( j < ir )
      {
        if ( a[indx[j-1]-1] < a[indx[j]-1] )
        {
          j = j + 1;
        }
      }

      if ( aval < a[indx[j-1]-1] )
      {
        indx[i-1] = indx[j-1];
        i = j;
        j = j + j;
      }
      else
      {
        j = ir + 1;
      }
    }
    indx[i-1] = indxt;
  }
}
//****************************************************************************80

int lrline ( double xu, double yu, double xv1, double yv1, double xv2, 
  double yv2, double dv )

//****************************************************************************80
//
//  Purpose:
//
//    LRLINE determines where a point lies in relation to a directed line.
//
//  Discussion:
//
//    LRLINE determines whether a point is to the left of, right of,
//    or on a directed line parallel to a line through given points.
//
//  Modified:
//
//    28 August 2003
//
//  Author:
//
//    Barry Joe,
//    Department of Computing Science,
//    University of Alberta,
//    Edmonton, Alberta, Canada  T6G 2H1
//
//  Reference:
//
//    Barry Joe,
//    GEOMPACK - a software package for the generation of meshes
//    using geometric algorithms,
//    Advances in Engineering Software,
//    Volume 13, pages 325-331, 1991.
//
//  Parameters:
//
//    Input, double XU, YU, XV1, YV1, XV2, YV2, are vertex coordinates; the
//    directed line is parallel to and at signed distance DV to the left of
//    the directed line from (XV1,YV1) to (XV2,YV2); (XU,YU) is the vertex for
//    which the position relative to the directed line is to be determined.
//
//    Input, double DV, the signed distance, positive for left.
//
//    Output, int LRLINE, is +1, 0, or -1 depending on whether (XU,YU) is
//    to the right of, on, or left of the directed line.  LRLINE is 0 if
//    the line degenerates to a point.
//
{
  double dx;
  double dxu;
  double dy;
  double dyu;
  double t;
  double tol = 0.0000001;
  double tolabs;
  int value;

  dx = xv2 - xv1;
  dy = yv2 - yv1;
  dxu = xu - xv1;
  dyu = yu - yv1;

  tolabs = tol * r8_max ( fabs ( dx ), 
                 r8_max ( fabs ( dy ), 
                 r8_max ( fabs ( dxu ), 
                 r8_max ( fabs ( dyu ), fabs ( dv ) ) ) ) );

  t = dy * dxu - dx * dyu + dv * sqrt ( dx * dx + dy * dy );

  if ( tolabs < t )
  {
    value = 1;
  }
  else if ( -tolabs <= t )
  {
    value = 0;
  }
  else if ( t < -tolabs )
  {
    value = -1;
  }

  return value;
}
//****************************************************************************80

void perm_inv ( int n, int p[] )

//****************************************************************************80
//
//  Purpose:
//
//    PERM_INV inverts a permutation "in place".
//
//  Modified:
//
//    13 January 2004
//
//  Parameters:
//
//    Input, int N, the number of objects being permuted.
//
//    Input/output, int P[N], the permutation, in standard index form.
//    On output, P describes the inverse permutation
//
{
  int i;
  int i0;
  int i1;
  int i2;
  int is;

  if ( n <= 0 )
  {
    cout << "\n";
    cout << "PERM_INV - Fatal error!\n";
    cout << "  Input value of N = " << n << "\n";
    exit ( 1 );
  }

  is = 1;

  for ( i = 1; i <= n; i++ )
  {
    i1 = p[i-1];

    while ( i < i1 )
    {
      i2 = p[i1-1];
      p[i1-1] = -i2;
      i1 = i2;
    }

    is = - i4_sign ( p[i-1] );
    p[i-1] = i4_sign ( is ) * abs ( p[i-1] );
  }

  for ( i = 1; i <= n; i++ )
  {
    i1 = -p[i-1];

    if ( 0 <= i1 )
    {
      i0 = i;

      for ( ; ; )
      {
        i2 = p[i1-1];
        p[i1-1] = i0;

        if ( i2 < 0 )
        {
          break;
        }
        i0 = i1;
        i1 = i2;
      }
    }
  }

  return;
}
//****************************************************************************80

double r8_epsilon ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_EPSILON returns the round off unit for double precision arithmetic.
//
//  Discussion:
//
//    R8_EPSILON is a number R which is a power of 2 with the property that,
//    to the precision of the computer's arithmetic,
//      1 < 1 + R
//    but 
//      1 = ( 1 + R / 2 )
//
//  Modified:
//
//    01 July 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_EPSILON, the double precision round-off unit.
//
{
  double r;

  r = 1.0;

  while ( 1.0 < ( double ) ( 1.0 + r )  )
  {
    r = r / 2.0;
  }

  return ( 2.0 * r );
}
//****************************************************************************80

double r8_huge ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_HUGE returns a "huge" double precision value.
//
//  Discussion:
//
//    HUGE_VAL is the largest representable legal double precision number, and is usually
//    defined in math.h, or sometimes in stdlib.h.
//
//  Modified:
//
//    31 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_HUGE, a "huge" double precision value.
//
{
  return HUGE_VAL;
}
//****************************************************************************80

double r8_max ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MAX returns the maximum of two R8's.
//
//  Modified:
//
//    10 January 2002
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MAX, the maximum of X and Y.
//
{
  if ( y < x )
  {
    return x;
  } 
  else
  {
    return y;
  }
}
//****************************************************************************80

double r8_min ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MIN returns the minimum of two R8's.
//
//  Modified:
//
//    09 May 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MIN, the minimum of X and Y.
//
{
  if ( y < x )
  {
    return y;
  } 
  else
  {
    return x;
  }
}
//****************************************************************************80

int r8_nint ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    R8_NINT returns the nearest integer to a double precision value.
//
//  Examples:
//
//        X         R8_NINT
//
//      1.3         1
//      1.4         1
//      1.5         1 or 2
//      1.6         2
//      0.0         0
//     -0.7        -1
//     -1.1        -1
//     -1.6        -2
//
//  Modified:
//
//    26 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, the value.
//
//    Output, int R8_NINT, the nearest integer to X.
//
{
  int s;
  int value;

  if ( x < 0.0 )
  {
    s = -1;
  }
  else
  {
    s = 1;
  }
  value = s * ( int ) ( fabs ( x ) + 0.5 );

  return value;
}
//****************************************************************************80*

void r82vec_permute ( int n, double a[], int p[] )

//****************************************************************************80*
//
//  Purpose:
//
//    R82VEC_PERMUTE permutes an R2 vector in place.
//
//  Discussion:
//
//    This routine permutes an array of real "objects", but the same
//    logic can be used to permute an array of objects of any arithmetic
//    type, or an array of objects of any complexity.  The only temporary
//    storage required is enough to store a single object.  The number
//    of data movements made is N + the number of cycles of order 2 or more,
//    which is never more than N + N/2.
//
//  Example:
//
//    Input:
//
//      N = 5
//      P = (   2,    4,    5,    1,    3 )
//      A = ( 1.0,  2.0,  3.0,  4.0,  5.0 )
//          (11.0, 22.0, 33.0, 44.0, 55.0 )
//
//    Output:
//
//      A    = (  2.0,  4.0,  5.0,  1.0,  3.0 )
//             ( 22.0, 44.0, 55.0, 11.0, 33.0 ).
//
//  Modified:
//
//    19 February 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of objects.
//
//    Input/output, double A[2*N], the array to be permuted.
//
//    Input, int P[N], the permutation.  P(I) = J means
//    that the I-th element of the output array should be the J-th
//    element of the input array.  P must be a legal permutation
//    of the integers from 1 to N, otherwise the algorithm will
//    fail catastrophically.
//
{
  double a_temp[2];
  int i;
  int iget;
  int iput;
  int istart;
//
//  Search for the next element of the permutation that has not been used.
//
  for ( istart = 1; istart <= n; istart++ )
  {
    if ( p[istart-1] < 0 )
    {
      continue;
    }
    else if ( p[istart-1] == istart )
    {
      p[istart-1] = -p[istart-1];
      continue;
    }
    else
    {
      a_temp[0] = a[0+(istart-1)*2];
      a_temp[1] = a[1+(istart-1)*2];
      iget = istart;
//
//  Copy the new value into the vacated entry.
//
      for ( ; ; )
      {
        iput = iget;
        iget = p[iget-1];

        p[iput-1] = -p[iput-1];

        if ( iget < 1 || n < iget )
        {
          cout << "\n";
          cout << "R82VEC_PERMUTE - Fatal error!\n";
          exit ( 1 );
        }

        if ( iget == istart )
        {
          a[0+(iput-1)*2] = a_temp[0];
          a[1+(iput-1)*2] = a_temp[1];
          break;
        }
        a[0+(iput-1)*2] = a[0+(iget-1)*2];
        a[1+(iput-1)*2] = a[1+(iget-1)*2];
      }
    }
  }
//
//  Restore the signs of the entries.
//
  for ( i = 0; i < n; i++ )
  {
    p[i] = -p[i];
  }

  return;
}
//****************************************************************************80

int *r82vec_sort_heap_index_a ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R82VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an R2 vector.
//
//  Discussion:
//
//    The sorting is not actually carried out.  Rather an index array is
//    created which defines the sorting.  This array may be used to sort
//    or index the array, or to sort or index related arrays keyed on the
//    original array.
//
//    Once the index array is computed, the sorting can be carried out
//    "implicitly:
//
//      A(1:2,INDX(I)), I = 1 to N is sorted,
//
//    or explicitly, by the call
//
//      call R82VEC_PERMUTE ( N, A, INDX )
//
//    after which A(1:2,I), I = 1 to N is sorted.
//
//  Modified:
//
//    13 January 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input, double A[2*N], an array to be index-sorted.
//
//    Output, int R82VEC_SORT_HEAP_INDEX_A[N], the sort index.  The
//    I-th element of the sorted array is A(0:1,R82VEC_SORT_HEAP_INDEX_A(I-1)).
//
{
  double aval[2];
  int i;
  int *indx;
  int indxt;
  int ir;
  int j;
  int l;

  if ( n < 1 )
  {
    return NULL;
  }

  if ( n == 1 )
  {
    indx = new int[1];
    indx[0] = 1;
    return indx;
  }

  indx = i4vec_indicator ( n );

  l = n / 2 + 1;
  ir = n;

  for ( ; ; )
  {
    if ( 1 < l )
    {
      l = l - 1;
      indxt = indx[l-1];
      aval[0] = a[0+(indxt-1)*2];
      aval[1] = a[1+(indxt-1)*2];
    }
    else
    {
      indxt = indx[ir-1];
      aval[0] = a[0+(indxt-1)*2];
      aval[1] = a[1+(indxt-1)*2];
      indx[ir-1] = indx[0];
      ir = ir - 1;

      if ( ir == 1 )
      {
        indx[0] = indxt;
        break;
      }

    }

    i = l;
    j = l + l;

    while ( j <= ir )
    {
      if ( j < ir )
      {
        if (   a[0+(indx[j-1]-1)*2] <  a[0+(indx[j]-1)*2] ||
             ( a[0+(indx[j-1]-1)*2] == a[0+(indx[j]-1)*2] &&
               a[1+(indx[j-1]-1)*2] <  a[1+(indx[j]-1)*2] ) )
        {
          j = j + 1;
        }
      }

      if (   aval[0] <  a[0+(indx[j-1]-1)*2] ||
           ( aval[0] == a[0+(indx[j-1]-1)*2] &&
             aval[1] <  a[1+(indx[j-1]-1)*2] ) )
      {
        indx[i-1] = indx[j-1];
        i = j;
        j = j + j;
      }
      else
      {
        j = ir + 1;
      }
    }
    indx[i-1] = indxt;
  }

  return indx;
}
//****************************************************************************80

void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
//
//  Modified:
//
//    11 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, double A[M*N], an M by N matrix to be printed.
//
//    Input, int ILO, JLO, the first row and column to print.
//
//    Input, int IHI, JHI, the last row and column to print.
//
//    Input, char *TITLE, an optional title.
//
{
# define INCX 5

  int i;
  int i2;
  int i2hi;
  int i2lo;
  int inc;
  int j;
  int j2hi;
  int j2lo;

  if ( 0 < s_len_trim ( title ) )
  {
    cout << "\n";
    cout << title << "\n";
  }

  for ( i2lo = i4_max ( ilo, 1 ); i2lo <= i4_min ( ihi, m ); i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    i2hi = i4_min ( i2hi, m );
    i2hi = i4_min ( i2hi, ihi );

    inc = i2hi + 1 - i2lo;

    cout << "\n";
    cout << "  Row: ";
    for ( i = i2lo; i <= i2hi; i++ )
    {
      cout << setw(7) << i << "       ";
    }
    cout << "\n";
    cout << "  Col\n";
    cout << "\n";

    j2lo = i4_max ( jlo, 1 );
    j2hi = i4_min ( jhi, n );

    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(5) << j << " ";
      for ( i2 = 1; i2 <= inc; i2++ )
      {
        i = i2lo - 1 + i2;
        cout << setw(14) << a[(i-1)+(j-1)*m];
      }
      cout << "\n";
    }
  }
  cout << "\n";

  return;
# undef INCX
}
//****************************************************************************80*

void s_blank_delete ( char *s )

//****************************************************************************80*
//
//  Purpose:
//
//    S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
//
//  Comment:
//
//    All TAB characters are also removed.
//
//  Modified:
//
//    05 May 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input/output, char *S, the string to be transformed.
//
{
  char *get;
  char *put;
  char TAB = 9;

  put = s;
  get = s;

  while ( *get != '\0' )
  {
    if ( *get != ' ' && *get != TAB )
    {
      *put = *get;
      put = put + 1;
    }

    get = get + 1;
  }

  *put = *get;

  return;
}
//****************************************************************************80

int s_index_last_c ( char *s, char c )

//****************************************************************************80
//
//  Purpose:
//
//    S_INDEX_LAST_C returns a pointer to the last occurrence of a given character.
//
//  Modified:
//
//    10 October 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a pointer to a string.
//
//    Input, char C, the character to search for.
//
//    Output, int S_INDEX_LAST_C, the index in S of the last occurrence of the character,
//    or -1 if it does not occur.
//
{
  int n;
  char *t;

  n = strlen ( s ) - 1;
  t = s + strlen ( s ) - 1;

  while ( 0 <= n ) 
  {
    if ( *t == c )
    {
      return n;
    }
    t--;
    n--;
  }

  return (-1);
}
//****************************************************************************80

int s_len_trim ( char *s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Modified:
//
//    26 April 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a pointer to a string.
//
//    Output, int S_LEN_TRIM, the length of the string to the last nonblank.
//    If S_LEN_TRIM is 0, then the string is entirely blank.
//
{
  int n;
  char* t;

  n = strlen ( s );
  t = s + strlen ( s ) - 1;

  while ( 0 < n ) 
  {
    if ( *t != ' ' )
    {
      return n;
    }
    t--;
    n--;
  }

  return n;
}
//****************************************************************************80

double s_to_r8 ( char *s, int *lchar, bool *error )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8 reads an R8 from a string.
//
//  Discussion:
//
//    This routine will read as many characters as possible until it reaches
//    the end of the string, or encounters a character which cannot be
//    part of the real number.
//
//    Legal input is:
//
//       1 blanks,
//       2 '+' or '-' sign,
//       2.5 spaces
//       3 integer part,
//       4 decimal point,
//       5 fraction part,
//       6 'E' or 'e' or 'D' or 'd', exponent marker,
//       7 exponent sign,
//       8 exponent integer part,
//       9 exponent decimal point,
//      10 exponent fraction part,
//      11 blanks,
//      12 final comma or semicolon.
//
//    with most quantities optional.
//
//  Examples:
//
//    S                 R
//
//    '1'               1.0
//    '     1   '       1.0
//    '1A'              1.0
//    '12,34,56'        12.0
//    '  34 7'          34.0
//    '-1E2ABCD'        -100.0
//    '-1X2ABCD'        -1.0
//    ' 2E-1'           0.2
//    '23.45'           23.45
//    '-4.2E+2'         -420.0
//    '17d2'            1700.0
//    '-14e-2'         -0.14
//    'e2'              100.0
//    '-12.73e-9.23'   -12.73 * 10.0**(-9.23)
//
//  Modified:
//
//    07 August 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, the string containing the
//    data to be read.  Reading will begin at position 1 and
//    terminate at the end of the string, or when no more
//    characters can be read to form a legal real.  Blanks,
//    commas, or other nonnumeric data will, in particular,
//    cause the conversion to halt.
//
//    Output, int *LCHAR, the number of characters read from
//    the string to form the number, including any terminating
//    characters such as a trailing comma or blanks.
//
//    Output, bool *ERROR, is true if an error occurred.
//
//    Output, double S_TO_R8, the real value that was read from the string.
//
{
  char c;
  int ihave;
  int isgn;
  int iterm;
  int jbot;
  int jsgn;
  int jtop;
  int nchar;
  int ndig;
  double r;
  double rbot;
  double rexp;
  double rtop;
  char TAB = 9;

  nchar = s_len_trim ( s );
  *error = false;
  r = 0.0;
  *lchar = -1;
  isgn = 1;
  rtop = 0.0;
  rbot = 1.0;
  jsgn = 1;
  jtop = 0;
  jbot = 1;
  ihave = 1;
  iterm = 0;

  for ( ; ; )
  {
    c = s[*lchar+1];
    *lchar = *lchar + 1;
//
//  Blank or TAB character.
//
    if ( c == ' ' || c == TAB )
    {
      if ( ihave == 2 )
      {
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        iterm = 1;
      }
      else if ( 1 < ihave )
      {
        ihave = 11;
      }
    }
//
//  Comma.
//
    else if ( c == ',' || c == ';' )
    {
      if ( ihave != 1 )
      {
        iterm = 1;
        ihave = 12;
        *lchar = *lchar + 1;
      }
    }
//
//  Minus sign.
//
    else if ( c == '-' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
        isgn = -1;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
        jsgn = -1;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Plus sign.
//
    else if ( c == '+' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Decimal point.
//
    else if ( c == '.' )
    {
      if ( ihave < 4 )
      {
        ihave = 4;
      }
      else if ( 6 <= ihave && ihave <= 8 )
      {
        ihave = 9;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Exponent marker.
//
    else if ( ch_eqi ( c, 'E' ) || ch_eqi ( c, 'D' ) )
    {
      if ( ihave < 6 )
      {
        ihave = 6;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Digit.
//
    else if ( ihave < 11 && '0' <= c && c <= '9' )
    {
      if ( ihave <= 2 )
      {
        ihave = 3;
      }
      else if ( ihave == 4 )
      {
        ihave = 5;
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        ihave = 8;
      }
      else if ( ihave == 9 )
      {
        ihave = 10;
      }

      ndig = ch_to_digit ( c );

      if ( ihave == 3 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
      }
      else if ( ihave == 5 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
        rbot = 10.0 * rbot;
      }
      else if ( ihave == 8 )
      {
        jtop = 10 * jtop + ndig;
      }
      else if ( ihave == 10 )
      {
        jtop = 10 * jtop + ndig;
        jbot = 10 * jbot;
      }

    }
//
//  Anything else is regarded as a terminator.
//
    else
    {
      iterm = 1;
    }
//
//  If we haven't seen a terminator, and we haven't examined the
//  entire string, go get the next character.
//
    if ( iterm == 1 || nchar <= *lchar + 1 )
    {
      break;
    }

  }
//
//  If we haven't seen a terminator, and we have examined the
//  entire string, then we're done, and LCHAR is equal to NCHAR.
//
  if ( iterm != 1 && (*lchar) + 1 == nchar )
  {
    *lchar = nchar;
  }
//
//  Number seems to have terminated.  Have we got a legal number?
//  Not if we terminated in states 1, 2, 6 or 7!
//
  if ( ihave == 1 || ihave == 2 || ihave == 6 || ihave == 7 )
  {
    *error = true;
    return r;
  }
//
//  Number seems OK.  Form it.
//
  if ( jtop == 0 )
  {
    rexp = 1.0;
  }
  else
  {
    if ( jbot == 1 )
    {
      rexp = pow ( 10.0, jsgn * jtop );
    }
    else
    {
      rexp = jsgn * jtop;
      rexp = rexp / jbot;
      rexp = pow ( 10.0, rexp );
    }

  }

  r = isgn * rexp * rtop / rbot;

  return r;
}
//****************************************************************************80

bool s_to_r8vec ( char *s, int n, double rvec[] )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8VEC reads an R8VEC from a string.
//
//  Modified:
//
//    19 February 2001
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, the string to be read.
//
//    Input, int N, the number of values expected.
//
//    Output, double RVEC[N], the values read from the string.
//
//    Output, bool S_TO_R8VEC, is true if an error occurred.
//
{
  bool error;
  int i;
  int lchar;
  double x;

  for ( i = 0; i < n; i++ )
  {
    rvec[i] = s_to_r8 ( s, &lchar, &error );

    if ( error )
    {
      return error;
    }

    s = s + lchar;

  }

  return error;
}
//****************************************************************************80

int s_word_count ( char *s )

//****************************************************************************80
//
//  Purpose:
//
//    S_WORD_COUNT counts the number of "words" in a string.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, the string to be examined.
//
//    Output, int S_WORD_COUNT, the number of "words" in the string.
//    Words are presumed to be separated by one or more blanks.
//
{
  bool blank;
  int i;
  int nword;

  nword = 0;
  blank = true;

  while ( *s ) 
  {
    if ( *s == ' ' )
    {
      blank = true;
    }
    else if ( blank )
    {
      nword = nword + 1;
      blank = false;
    }
    *s++;
  }

  return nword;
}
//****************************************************************************80

int swapec ( int i, int *top, int *btri, int *bedg, int point_num, 
  double point_xy[], int tri_num, int tri_vert[], int tri_nabe[], 
  int stack[] )

//****************************************************************************80
//
//  Purpose:
//
//    SWAPEC swaps diagonal edges until all triangles are Delaunay.
//
//  Discussion:
//
//    The routine swaps diagonal edges in a 2D triangulation, based on
//    the empty circumcircle criterion, until all triangles are Delaunay,
//    given that I is the index of the new vertex added to the triangulation.
//
//  Modified:
//
//    03 September 2003
//
//  Author:
//
//    Barry Joe,
//    Department of Computing Science,
//    University of Alberta,
//    Edmonton, Alberta, Canada  T6G 2H1
//
//  Reference:
//
//    Barry Joe,
//    GEOMPACK - a software package for the generation of meshes
//    using geometric algorithms,
//    Advances in Engineering Software,
//    Volume 13, pages 325-331, 1991.
//
//  Parameters:
//
//    Input, int I, the index of the new vertex.
//
//    Input/output, int *TOP, the index of the top of the stack.
//    On output, TOP is zero.
//
//    Input/output, int *BTRI, *BEDG; on input, if positive, are the
//    triangle and edge indices of a boundary edge whose updated indices
//    must be recorded.  On output, these may be updated because of swaps.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, double POINT_XY[POINT_NUM*2], the coordinates of the points.
//
//    Input, int TRI_NUM, the number of triangles.
//
//    Input/output, int TRI_VERT[TRI_NUM*3], the triangle incidence list.
//    May be updated on output because of swaps.
//
//    Input/output, int TRI_NABE[TRI_NUM*3], the triangle neighbor list;
//    negative values are used for links of the counter-clockwise linked
//    list of boundary edges;  May be updated on output because of swaps.
//
//      LINK = -(3*I + J-1) where I, J = triangle, edge index.
//
//    Workspace, int STACK[MAXST]; on input, entries 1 through TOP
//    contain the indices of initial triangles (involving vertex I)
//    put in stack; the edges opposite I should be in interior;  entries
//    TOP+1 through MAXST are used as a stack.
//
//    Output, int SWAPEC, is set to 8 for abnormal return.
//
{
  int a;
  int b;
  int c;
  int e;
  int ee;
  int em1;
  int ep1;
  int f;
  int fm1;
  int fp1;
  int l;
  int r;
  int s;
  int swap;
  int t;
  int tt;
  int u;
  double x;
  double y;
//
//  Determine whether triangles in stack are Delaunay, and swap
//  diagonal edge of convex quadrilateral if not.
//
  x = point_xy[2*(i-1)+0];
  y = point_xy[2*(i-1)+1];

  for ( ; ; )
  {
    if ( *top <= 0 ) 
    {
      break;
    }

    t = stack[(*top)-1];
    *top = *top - 1;

    if ( tri_vert[3*(t-1)+0] == i )
    {
      e = 2;
      b = tri_vert[3*(t-1)+2];
    }
    else if ( tri_vert[3*(t-1)+1] == i )
    {
      e = 3;
      b = tri_vert[3*(t-1)+0];
    }
    else
    {
      e = 1;
      b = tri_vert[3*(t-1)+1];
    }

    a = tri_vert[3*(t-1)+e-1];
    u = tri_nabe[3*(t-1)+e-1];

    if ( tri_nabe[3*(u-1)+0] == t )
    {
      f = 1;
      c = tri_vert[3*(u-1)+2];
    }
    else if ( tri_nabe[3*(u-1)+1] == t )
    {
      f = 2;
      c = tri_vert[3*(u-1)+0];
    }
    else
    {
      f = 3;
      c = tri_vert[3*(u-1)+1];
    }

    swap = diaedg ( x, y, 
      point_xy[2*(a-1)+0], point_xy[2*(a-1)+1],
      point_xy[2*(c-1)+0], point_xy[2*(c-1)+1],
      point_xy[2*(b-1)+0], point_xy[2*(b-1)+1] );

    if ( swap == 1 )
    {
      em1 = i4_wrap ( e - 1, 1, 3 );
      ep1 = i4_wrap ( e + 1, 1, 3 );
      fm1 = i4_wrap ( f - 1, 1, 3 );
      fp1 = i4_wrap ( f + 1, 1, 3 );

      tri_vert[3*(t-1)+ep1-1] = c;
      tri_vert[3*(u-1)+fp1-1] = i;
      r = tri_nabe[3*(t-1)+ep1-1];
      s = tri_nabe[3*(u-1)+fp1-1];
      tri_nabe[3*(t-1)+ep1-1] = u;
      tri_nabe[3*(u-1)+fp1-1] = t;
      tri_nabe[3*(t-1)+e-1] = s;
      tri_nabe[3*(u-1)+f-1] = r;

      if ( 0 < tri_nabe[3*(u-1)+fm1-1] )
      {
        *top = *top + 1;
        stack[(*top)-1] = u;
      }

      if ( 0 < s )
      {
        if ( tri_nabe[3*(s-1)+0] == u )
        {
          tri_nabe[3*(s-1)+0] = t;
        }
        else if ( tri_nabe[3*(s-1)+1] == u )
        {
          tri_nabe[3*(s-1)+1] = t;
        }
        else
        {
          tri_nabe[3*(s-1)+2] = t;
        }

        *top = *top + 1;

        if ( point_num < *top )
        {
          return 8;
        }

        stack[(*top)-1] = t;
      }
      else
      {
        if ( u == *btri && fp1 == *bedg )
        {
          *btri = t;
          *bedg = e;
        }

        l = - ( 3 * t + e - 1 );
        tt = t;
        ee = em1;

        while ( 0 < tri_nabe[3*(tt-1)+ee-1] )
        {
          tt = tri_nabe[3*(tt-1)+ee-1];

          if ( tri_vert[3*(tt-1)+0] == a )
          {
            ee = 3;
          }
          else if ( tri_vert[3*(tt-1)+1] == a )
          {
            ee = 1;
          }
          else
          {
            ee = 2;
          }

        }

        tri_nabe[3*(tt-1)+ee-1] = l;

      }

      if ( 0 < r )
      {
        if ( tri_nabe[3*(r-1)+0] == t )
        {
          tri_nabe[3*(r-1)+0] = u;
        }
        else if ( tri_nabe[3*(r-1)+1] == t )
        {
          tri_nabe[3*(r-1)+1] = u;
        }
        else
        {
          tri_nabe[3*(r-1)+2] = u;
        }
      }
      else
      {
        if ( t == *btri && ep1 == *bedg )
        {
          *btri = u;
          *bedg = f;
        }

        l = - ( 3 * u + f - 1 );
        tt = u;
        ee = fm1;

        while ( 0 < tri_nabe[3*(tt-1)+ee-1] )
        {
          tt = tri_nabe[3*(tt-1)+ee-1];

          if ( tri_vert[3*(tt-1)+0] == b )
          {
            ee = 3;
          }
          else if ( tri_vert[3*(tt-1)+1] == b )
          {
            ee = 1;
          }
          else
          {
            ee = 2;
          }

        }

        tri_nabe[3*(tt-1)+ee-1] = l;

      }

    }

  }

  return 0;
}
//****************************************************************************80

void timestamp ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    21 August 2002
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 29

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  size_t len;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  len = strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  if ( len != 0 )
  {
    cout << time_buffer << "\n";
  }

  return;
# undef TIME_SIZE
}
//****************************************************************************80

char *timestring ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTRING returns the current YMDHMS date as a string.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, char *TIMESTRING, a string containing the current YMDHMS date.
//
{
# define TIME_SIZE 29

  const struct tm *tm;
  size_t len;
  time_t now;
  char *s;

  now = time ( NULL );
  tm = localtime ( &now );

  s = new char[TIME_SIZE];

  len = strftime ( s, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  return s;
# undef TIME_SIZE
}
//****************************************************************************80

void triangulation_order3_plot_eps ( char *file_name, int node_num, 
  double node_xy[], int triangle_num, int triangle_node[], int node_show, 
  int triangle_show )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGULATION_ORDER3_PLOT_EPS plots a triangulation of a set of nodes.
//
//  Discussion:
//
//    The triangulation is most usually a Delaunay triangulation,
//    but this is not necessary.
//
//  Modified:
//
//    16 March 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *FILE_NAME, the name of the output file.
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the nodes.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[3*TRIANGLE_NUM], lists, for each triangle,
//    the indices of the nodes that form the vertices of the triangle.
//
//    Input, int NODE_SHOW:
//    0, do not show nodes;
//    1, show nodes;
//    2, show nodes and label them.
//
//    Input, int TRIANGLE_SHOW:
//    0, do not show triangles;
//    1, show triangles;
//    2, show triangles and label them.
//
//  Local parameters:
//
//    int CIRCLE_SIZE, controls the size of the circles depicting
//    the nodes.  Currently set to 5.  3 is pretty small, and 1 is
//    barely visible.
//
{
  double ave_x;
  double ave_y;
  int circle_size = 3;
  char *date_time;
  int delta;
  int e;
  ofstream file_unit;
  int i;
  int node;
  int triangle;
  double x_max;
  double x_min;
  int x_ps;
  int x_ps_max = 576;
  int x_ps_max_clip = 594;
  int x_ps_min = 36;
  int x_ps_min_clip = 18;
  double x_scale;
  double y_max;
  double y_min;
  int y_ps;
  int y_ps_max = 666;
  int y_ps_max_clip = 684;
  int y_ps_min = 126;
  int y_ps_min_clip = 108;
  double y_scale;

  date_time = timestring ( );
//
//  We need to do some figuring here, so that we can determine
//  the range of the data, and hence the height and width
//  of the piece of paper.
//
  x_max = -r8_huge ( );
  for ( node = 0; node < node_num; node++ )
  {
     if ( x_max < node_xy[0+node*2] )
     {
       x_max = node_xy[0+node*2];
     }
  }
  x_min = r8_huge ( );
  for ( node = 0; node < node_num; node++ )
  {
     if ( node_xy[0+node*2] < x_min )
     {
       x_min = node_xy[0+node*2];
     }
  }
  x_scale = x_max - x_min;

  x_max = x_max + 0.05 * x_scale;
  x_min = x_min - 0.05 * x_scale;
  x_scale = x_max - x_min;

  y_max = -r8_huge ( );
  for ( node = 0; node < node_num; node++ )
  {
     if ( y_max < node_xy[1+node*2] )
     {
       y_max = node_xy[1+node*2];
     }
  }
  y_min = r8_huge ( );
  for ( node = 0; node < node_num; node++ )
  {
     if ( node_xy[1+node*2] < y_min )
     {
       y_min = node_xy[1+node*2];
     }
  }
  y_scale = y_max - y_min;

  y_max = y_max + 0.05 * y_scale;
  y_min = y_min - 0.05 * y_scale;
  y_scale = y_max - y_min;

  if ( x_scale < y_scale )
  {
    delta = r8_nint ( ( double ) ( x_ps_max - x_ps_min )
      * ( y_scale - x_scale ) / ( 2.0 * y_scale ) );

    x_ps_max = x_ps_max - delta;
    x_ps_min = x_ps_min + delta;

    x_ps_max_clip = x_ps_max_clip - delta;
    x_ps_min_clip = x_ps_min_clip + delta;

    x_scale = y_scale;
  }
  else if ( y_scale < x_scale )
  {
    delta = r8_nint ( ( double ) ( y_ps_max - y_ps_min ) 
      * ( x_scale - y_scale ) / ( 2.0 * x_scale ) );

    y_ps_max = y_ps_max - delta;
    y_ps_min = y_ps_min + delta;

    y_ps_max_clip = y_ps_max_clip - delta;
    y_ps_min_clip = y_ps_min_clip + delta;

    y_scale = x_scale;
  }

  file_unit.open ( file_name );

  if ( !file_unit )
  {
    cout << "\n";
    cout << "TRIANGULATION_ORDER3_PLOT_EPS - Fatal error!\n";
    cout << "  Could not open the output EPS file.\n";
    exit ( 1 );
  }

  file_unit << "%!PS-Adobe-3.0 EPSF-3.0\n";
  file_unit << "%%Creator: triangulation_order3_plot_eps.C\n";
  file_unit << "%%Title: " << file_name << "\n";
  file_unit << "%%CreationDate: " << date_time << "\n";
  delete [] date_time;

  file_unit << "%%Pages: 1\n";
  file_unit << "%%BoundingBox:  "
    << x_ps_min << "  "
    << y_ps_min << "  "
    << x_ps_max << "  "
    << y_ps_max << "\n";
  file_unit << "%%Document-Fonts: Times-Roman\n";
  file_unit << "%%LanguageLevel: 1\n";
  file_unit << "%%EndComments\n";
  file_unit << "%%BeginProlog\n";
  file_unit << "/inch {72 mul} def\n";
  file_unit << "%%EndProlog\n";
  file_unit << "%%Page:      1     1\n";
  file_unit << "save\n";
  file_unit << "%\n";
  file_unit << "% Set the RGB line color to very light gray.\n";
  file_unit << "%\n";
  file_unit << " 0.9000 0.9000 0.9000 setrgbcolor\n";
  file_unit << "%\n";
  file_unit << "% Draw a gray border around the page.\n";
  file_unit << "%\n";
  file_unit << "newpath\n";
  file_unit << x_ps_min << "  "
            << y_ps_min << "  moveto\n";
  file_unit << x_ps_max << "  "
            << y_ps_min << "  lineto\n";
  file_unit << x_ps_max << "  "
            << y_ps_max << "  lineto\n";
  file_unit << x_ps_min << "  "
            << y_ps_max << "  lineto\n";
  file_unit << x_ps_min << "  "
            << y_ps_min << "  lineto\n";
  file_unit << "stroke\n";
  file_unit << "%\n";
  file_unit << "% Set RGB line color to black.\n";
  file_unit << "%\n";
  file_unit << " 0.0000 0.0000 0.0000 setrgbcolor\n";
  file_unit << "%\n";
  file_unit << "%  Set the font and its size:\n";
  file_unit << "%\n";
  file_unit << "/Times-Roman findfont\n";
  file_unit << "0.50 inch scalefont\n";
  file_unit << "setfont\n";
  file_unit << "%\n";
  file_unit << "%  Print a title:\n";
  file_unit << "%\n";
  file_unit << "%  210  702 moveto\n";
  file_unit << "%(Pointset) show\n";
  file_unit << "%\n";
  file_unit << "% Define a clipping polygon\n";
  file_unit << "%\n";
  file_unit << "newpath\n";
  file_unit << x_ps_min_clip << "  "
            << y_ps_min_clip << "  moveto\n";
  file_unit << x_ps_max_clip << "  "
            << y_ps_min_clip << "  lineto\n";
  file_unit << x_ps_max_clip << "  "
            << y_ps_max_clip << "  lineto\n";
  file_unit << x_ps_min_clip << "  "
            << y_ps_max_clip << "  lineto\n";
  file_unit << x_ps_min_clip << "  "
            << y_ps_min_clip << "  lineto\n";
  file_unit << "clip newpath\n";
//
//  Draw the nodes.
//
  if ( 1 <= node_show )
  {
    file_unit << "%\n";
    file_unit << "%  Draw filled dots at each node:\n";
    file_unit << "%\n";
    file_unit << "%  Set the color to blue:\n";
    file_unit << "%\n";
    file_unit << "0.000  0.150  0.750  setrgbcolor\n";
    file_unit << "%\n";

    for ( node = 0; node < node_num; node++ )
    {
      x_ps = ( int ) (
        ( ( x_max - node_xy[0+node*2]         ) * ( double ) ( x_ps_min )  
        + (       + node_xy[0+node*2] - x_min ) * ( double ) ( x_ps_max ) ) 
        / ( x_max                     - x_min ) );

      y_ps = ( int ) (
        ( ( y_max - node_xy[1+node*2]         ) * ( double ) ( y_ps_min )  
        + (         node_xy[1+node*2] - y_min ) * ( double ) ( y_ps_max ) ) 
        / ( y_max                     - y_min ) );

      file_unit << "newpath  " 
        << x_ps << "  " 
        << y_ps << "  "
        << circle_size << " 0 360 arc closepath fill\n";
    }
  }
//
//  Label the nodes.
//
  if ( 2 <= node_show )
  {
    file_unit << "%\n";
    file_unit << "%  Label the nodes:\n";
    file_unit << "%\n";
    file_unit << "%  Set the color to darker blue:\n";
    file_unit << "%\n";
    file_unit << "0.000  0.250  0.850  setrgbcolor\n";
    file_unit << "/Times-Roman findfont\n";
    file_unit << "0.20 inch scalefont\n";
    file_unit << "setfont\n";

    file_unit << "%\n";

    for ( node = 0; node < node_num; node++ )
    { 
      x_ps = ( int ) (
        ( ( x_max - node_xy[0+node*2]         ) * ( double ) ( x_ps_min )  
        + (       + node_xy[0+node*2] - x_min ) * ( double ) ( x_ps_max ) ) 
        / ( x_max                     - x_min ) );

      y_ps = ( int ) (
        ( ( y_max - node_xy[1+node*2]         ) * ( double ) ( y_ps_min )  
        + (         node_xy[1+node*2] - y_min ) * ( double ) ( y_ps_max ) ) 
        / ( y_max                     - y_min ) );

      file_unit << "newpath  " 
        << x_ps     << "  " 
        << y_ps + 5 << "  moveto ("
        << node+1   << ") show\n";
    }
  }
//
//  Draw the triangles.
//
  if ( 1 <= triangle_show )
  {
    file_unit << "%\n";
    file_unit << "%  Set the RGB color to red.\n";
    file_unit << "%\n";
    file_unit << "0.900  0.200  0.100 setrgbcolor\n";
    file_unit << "%\n";
    file_unit << "%  Draw the triangles.\n";
    file_unit << "%\n";

    for ( triangle = 0; triangle < triangle_num; triangle++ )
    {
      file_unit << "newpath\n";

      for ( i = 1; i <= 4; i++ )
      {
        e = i4_wrap ( i, 1, 3 );

        node = triangle_node[e-1+triangle*3] - 1;

        x_ps = ( int ) (
          ( ( x_max - node_xy[0+node*2]         ) * ( double ) ( x_ps_min )  
          + (       + node_xy[0+node*2] - x_min ) * ( double ) ( x_ps_max ) ) 
          / ( x_max                     - x_min ) );

        y_ps = ( int ) (
          ( ( y_max - node_xy[1+node*2]         ) * ( double ) ( y_ps_min )  
          + (         node_xy[1+node*2] - y_min ) * ( double ) ( y_ps_max ) ) 
          / ( y_max                     - y_min ) );

        if ( i == 1 )
        {
          file_unit << x_ps << "  " << y_ps << "  moveto\n";
        } 
        else
        {
          file_unit << x_ps << "  " << y_ps << "  lineto\n";
        }
      }
      file_unit << "stroke\n";
    }
  }
//
//  Label the triangles.
//
  if ( 2 <= triangle_show )
  {
    file_unit << "%\n";
    file_unit << "%  Label the triangles.\n";
    file_unit << "%\n";
    file_unit << "%  Set the RGB color to darker red.\n";
    file_unit << "%\n";
    file_unit << "0.950  0.250  0.150 setrgbcolor\n";
    file_unit << "/Times-Roman findfont\n";
    file_unit << "0.20 inch scalefont\n";
    file_unit << "setfont\n";
    file_unit << "%\n";

    for ( triangle = 0; triangle < triangle_num; triangle++ )
    {
      ave_x = 0.0;
      ave_y = 0.0;

      for ( i = 1; i <= 3; i++ )
      {
        node = triangle_node[i-1+triangle*3] - 1;
        ave_x = ave_x + node_xy[0+node*2];
        ave_y = ave_y + node_xy[1+node*2];
      }
      ave_x = ave_x / 3.0;
      ave_y = ave_y / 3.0;

      x_ps = ( int ) (
        ( ( x_max - ave_x         ) * ( double ) ( x_ps_min )  
        + (       + ave_x - x_min ) * ( double ) ( x_ps_max ) ) 
        / ( x_max         - x_min ) );

      y_ps = ( int ) (
        ( ( y_max - ave_y         ) * ( double ) ( y_ps_min )  
        + (         ave_y - y_min ) * ( double ) ( y_ps_max ) ) 
        / ( y_max         - y_min ) );

      file_unit << x_ps << "  " 
                << y_ps << "  moveto ("
                << triangle+1 << ") show\n";
    }
  }

  file_unit << "%\n";
  file_unit << "restore  showpage\n";
  file_unit << "%\n";
  file_unit << "%  End of page.\n";
  file_unit << "%\n";
  file_unit << "%%Trailer\n";
  file_unit << "%%EOF\n";

  file_unit.close ( );

  return;
}
//****************************************************************************80

void vbedg ( double x, double y, int point_num, double point_xy[], int tri_num, 
  int tri_vert[], int tri_nabe[], int *ltri, int *ledg, int *rtri, int *redg )

//****************************************************************************80
//
//  Purpose:
//
//    VBEDG determines which boundary edges are visible to a point.
//
//  Discussion:
//
//    The point (X,Y) is assumed to be outside the convex hull of the
//    region covered by the 2D triangulation.
//
//  Author:
//
//    Barry Joe,
//    Department of Computing Science,
//    University of Alberta,
//    Edmonton, Alberta, Canada  T6G 2H1
//
//  Reference:
//
//    Barry Joe,
//    GEOMPACK - a software package for the generation of meshes
//    using geometric algorithms,
//    Advances in Engineering Software,
//    Volume 13, pages 325-331, 1991.
//
//  Modified:
//
//    02 September 2003
//
//  Parameters:
//
//    Input, double X, Y, the coordinates of a point outside the convex hull
//    of the current triangulation.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, double POINT_XY[POINT_NUM*2], the coordinates of the vertices.
//
//    Input, int TRI_NUM, the number of triangles.
//
//    Input, int TRI_VERT[TRI_NUM*3], the triangle incidence list.
//
//    Input, int TRI_NABE[TRI_NUM*3], the triangle neighbor list; negative
//    values are used for links of a counter clockwise linked list of boundary
//    edges;
//      LINK = -(3*I + J-1) where I, J = triangle, edge index.
//
//    Input/output, int *LTRI, *LEDG.  If LTRI != 0 then these values are
//    assumed to be already computed and are not changed, else they are updated.
//    On output, LTRI is the index of boundary triangle to the left of the
//    leftmost boundary triangle visible from (X,Y), and LEDG is the boundary
//    edge of triangle LTRI to the left of the leftmost boundary edge visible
//    from (X,Y).  1 <= LEDG <= 3.
//
//    Input/output, int *RTRI.  On input, the index of the boundary triangle
//    to begin the search at.  On output, the index of the rightmost boundary
//    triangle visible from (X,Y).
//
//    Input/output, int *REDG, the edge of triangle RTRI that is visible
//    from (X,Y).  1 <= REDG <= 3.
//
{
  int a;
  double ax;
  double ay;
  int b;
  double bx;
  double by;
  bool done;
  int e;
  int l;
  int lr;
  int t;
//
//  Find the rightmost visible boundary edge using links, then possibly
//  leftmost visible boundary edge using triangle neighbor information.
//
  if ( *ltri == 0 )
  {
    done = false;
    *ltri = *rtri;
    *ledg = *redg;
  }
  else
  {
    done = true;
  }

  for ( ; ; )
  {
    l = -tri_nabe[3*((*rtri)-1)+(*redg)-1];
    t = l / 3;
    e = 1 + l % 3;
    a = tri_vert[3*(t-1)+e-1];

    if ( e <= 2 )
    {
      b = tri_vert[3*(t-1)+e];
    }
    else
    {
      b = tri_vert[3*(t-1)+0];
    }

    ax = point_xy[2*(a-1)+0];
    ay = point_xy[2*(a-1)+1];

    bx = point_xy[2*(b-1)+0];
    by = point_xy[2*(b-1)+1];

    lr = lrline ( x, y, ax, ay, bx, by, 0.0 );

    if ( lr <= 0 )
    {
      break;
    }

    *rtri = t;
    *redg = e;

  }

  if ( done )
  {
    return;
  }

  t = *ltri;
  e = *ledg;

  for ( ; ; )
  {
    b = tri_vert[3*(t-1)+e-1];
    e = i4_wrap ( e-1, 1, 3 );

    while ( 0 < tri_nabe[3*(t-1)+e-1] )
    {
      t = tri_nabe[3*(t-1)+e-1];

      if ( tri_vert[3*(t-1)+0] == b )
      {
        e = 3;
      }
      else if ( tri_vert[3*(t-1)+1] == b )
      {
        e = 1;
      }
      else
      {
        e = 2;
      }

    }

    a = tri_vert[3*(t-1)+e-1];
    ax = point_xy[2*(a-1)+0];
    ay = point_xy[2*(a-1)+1];

    bx = point_xy[2*(b-1)+0];
    by = point_xy[2*(b-1)+1];

    lr = lrline ( x, y, ax, ay, bx, by, 0.0 );

    if ( lr <= 0 )
    {
      break;
    }

  }

  *ltri = t;
  *ledg = e;

  return;
}