function [ x, y, w ] = rule07 ( )

%*****************************************************************************80
%
%% rule07() returns the quadrilateral rule of precision 7.
%
%  Discussion:
%
%    We suppose we are given a quadrilateral Quad with vertices
%    (0,0), (1,0), (1,1), (0,1),
%    We call a rule with n points, returning coordinates
%    x, y, and weights w.  Then the integral I of f(x,y,z) over Quad is 
%    approximated by Q as follows:
%
%    Q = area(Quad) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i)) 
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    29 April 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Freddie Witherden, Peter Vincent,
%    On the identification of symmetric quadrature rules for finite element methods,
%    Computers and Mathematics with Applications,
%    Volume 69, pages 1232-1241, 2015.
%
%  Output:
%
%    real x(n), y(n): the coordinates of quadrature points.
%
%    real w(n): the quadrature weights, which sum to 1.
%
  x = [ ...
          0.9629100498862757, ...
          0.5000000000000000, ...
          0.0370899501137243, ...
          0.5000000000000000, ...
          0.9029898914592993, ...
          0.9029898914592993, ...
          0.0970101085407006, ...
          0.0970101085407006, ...
          0.6902772166041579, ...
          0.6902772166041579, ...
          0.3097227833958421, ...
          0.3097227833958421 ];

  y = [ ...
          0.5000000000000000, ...
          0.9629100498862757, ...
          0.5000000000000000, ...
          0.0370899501137243, ...
          0.9029898914592993, ...
          0.0970101085407006, ...
          0.9029898914592993, ...
          0.0970101085407006, ...
          0.6902772166041579, ...
          0.3097227833958421, ...
          0.6902772166041579, ...
          0.3097227833958421 ];

  w = [ ...
          0.0604938271604938, ...
          0.0604938271604938, ...
          0.0604938271604938, ...
          0.0604938271604938, ...
          0.0593579436726576, ...
          0.0593579436726576, ...
          0.0593579436726576, ...
          0.0593579436726576, ...
          0.1301482291668486, ...
          0.1301482291668486, ...
          0.1301482291668486, ...
          0.1301482291668486 ];

  return
end
