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

using namespace std;

# include "triangle_interpolate.hpp"

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

void r8vec_uniform_01 ( int n, int &seed, double r[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    19 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Second Edition,
//    Springer, 1987,
//    ISBN: 0387964673,
//    LC: QA76.9.C65.B73.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, December 1986, pages 362-376.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998,
//    ISBN: 0471134031,
//    LC: T57.62.H37.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, Number 2, 1969, pages 136-143.
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double R[N], the vector of pseudorandom values.
//
{
  int i;
  const int i4_huge = 2147483647;
  int k;

  if ( seed == 0 )
  {
    cerr << "\n";
    cerr << "R8VEC_UNIFORM_01 - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  for ( i = 0; i < n; i++ )
  {
    k = seed / 127773;

    seed = 16807 * ( seed - k * 127773 ) - k * 2836;

    if ( seed < 0 )
    {
      seed = seed + i4_huge;
    }

    r[i] = ( double ) ( seed ) * 4.656612875E-10;
  }

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

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

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

double triangle_area ( double p1x, double p1y, double p2x, double p2y, 
  double p3x, double p3y )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGLE_AREA computes the area of a triangle in 2D.
//
//  Discussion:
//
//    If the triangle's vertices are given in counter clockwise order,
//    the area will be positive.  If the triangle's vertices are given
//    in clockwise order, the area will be negative!
//
//    An earlier version of this routine always returned the absolute
//    value of the computed area.  I am convinced now that that is
//    a less useful result!  For instance, by returning the signed 
//    area of a triangle, it is possible to easily compute the area 
//    of a nonconvex polygon as the sum of the (possibly negative) 
//    areas of triangles formed by node 1 and successive pairs of vertices.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    17 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double P1X, P1Y, P2X, P2Y, P3X, P3Y, the coordinates
//    of the vertices P1, P2, and P3.
//
//    Output, double TRIANGLE_AREA, the area of the triangle.
//
{
  double area;

  area = 0.5 * ( 
    p1x * ( p2y - p3y ) + 
    p2x * ( p3y - p1y ) + 
    p3x * ( p1y - p2y ) );
 
  return area;
}
//****************************************************************************80

double *triangle_interpolate_linear ( int m, int n, double p1[2], double p2[2], 
  double p3[2], double p[2], double v1[], double v2[], double v3[] )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGLE_INTERPOLATE_LINEAR interpolates data given on a triangle's vertices.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    19 January 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the dimension of the quantity.
//
//    Input, int N, the number of points.
//
//    Input, double P1[2], P2[2], P3[2], the vertices of the triangle,
//    in counterclockwise order.
//
//    Input, double P[2*N], the point at which the interpolant is desired.
//
//    Input, double V1[M], V2[M], V3[M], the value of some quantity at the vertices.
//
//    Output, double TRIANGLE_INTERPOLATE_LINEAR[M,N], the interpolated value 
//    of the quantity at P.
//
{
  double abc;
  double apc;
  double abp;
  int i;
  int j;
  double pbc;
  double *v;

  v = new double[m*n];

  abc = triangle_area ( p1[0], p1[1], p2[0], p2[1], p3[0], p3[1] );

  for ( j = 0; j < n; j++ )
  {
    pbc = triangle_area ( p[0+j*2], p[1+j*2], p2[0],    p2[1],    p3[0],    p3[1] );
    apc = triangle_area ( p1[0],    p1[1],    p[0+j*2], p[1+j*2], p3[0],    p3[1] );
    abp = triangle_area ( p1[0],    p1[1],    p2[0],    p2[1],    p[0+j*2], p[1+j*2] );
    for ( i = 0; i < m; i++ )
    {
      v[i+j*m] =
      ( pbc * v1[i]
      + apc * v2[i]
      + abp * v3[i] )
      / abc;
    }
  }

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

double *uniform_in_triangle_map1 ( double v1[2], double v2[2], double v3[2],
  int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    UNIFORM_IN_TRIANGLE_MAP1 maps uniform points into a triangle.
//
//  Discussion:
//
//    This routine uses Turk's rule 1.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    18 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Greg Turk,
//    Generating Random Points in a Triangle,
//    in Graphics Gems,
//    edited by Andrew Glassner,
//    AP Professional, 1990, pages 24-28.
//
//  Parameters:
//
//    Input, double V1[2], V2[2], V3[2], the vertices.
//
//    Input, int N, the number of points.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double UNIFORM_IN_TRIANGLE_MAP1[2*N], the points.
//
{
  double a;
  double b;
  double c;
  int i;
  int j;
  double r[2];
  double *x;

  x = new double[2*n];

  for ( j = 0; j < n; j++ )
  {
    r8vec_uniform_01 ( 2, seed, r );

    r[1] = sqrt ( r[1] );

    a = 1.0 - r[1];
    b = ( 1.0 - r[0] ) * r[1];
    c = r[0] * r[1];

    for ( i = 0; i < 2; i++ )
    {
      x[i+j*2] = a * v1[i] + b * v2[i] + c * v3[i];
    }
  }

  return x;
}