function inside = polygon_contains_point_2d ( n, v, p )
% POLYGON_CONTAINS_POINT_2D finds if a point is inside a simple polygon in 2D.
%
%  Discussion:
%
%    A simple polygon is one whose boundary never crosses itself.
%    The polygon does not need to be convex.
%
%  Modified:
%
%    09 May 2005
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    M Shimrat,
%    Position of Point Relative to Polygon,
%    ACM Algorithm 112,
%    Communications of the ACM,
%    Volume 5, Number 8, page 434, August 1962.
%
%  Parameters:
%
%    Input, integer N, the number of nodes or vertices in the polygon.
%    N must be at least 3.
%
%    Input, real V(2,N), the coordinates of the vertices of the polygon.
%
%    Input, real P(2), the coordinates of the point to be tested.
%
%    Output, logical INSIDE, is TRUE if the point is inside the polygon.
%
  inside = 0;

  for i = 1 : n

    x1 = v(1,i);
    y1 = v(2,i);

    if ( i < n )
      x2 = v(1,i+1);
      y2 = v(2,i+1);
    else
      x2 = v(1,1);
      y2 = v(2,1);
    end

    if ( ( y1 < p(2) & p(2) <= y2 ) | ( p(2) <= y1 & y2 < p(2) ) )
      if ( ( p(1) - x1 ) - ( p(2) - y1 ) * ( x2 - x1 ) / ( y2 - y1 ) < 0.0 )
        inside = ~inside;
      end
    end
  end
  