function area = polygon_area_3d_2 ( n, v, area )
%*****************************************************************************80
%
%% POLYGON_AREA_3D_2 computes the area of a polygon in 3D.
%
% Discussion:
%
% The computation is not valid unless the vertices of the polygon
% lie in a plane, so that the polygon that is defined is "flat".
%
% The polygon does not have to be "regular", that is, neither its
% sides nor its angles need to be equal.
%
% The area is computed as the sum of the areas of the triangles
% formed by the last node with consecutive pairs of nodes (1,2),
% (2,3), ..., and (N-2,N-1).
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 18 October 2005
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Adrian Bowyer and John Woodwark,
% A Programmer's Geometry,
% Butterworths, 1983.
%
% Input:
%
% integer N, the number of vertices of the polygon.
%
% real V(3,N), the coordinates of the vertices.
%
% Output:
%
% real AREA, the area of the polygon.
%
area_vector = zeros ( 3, 1 );
for i = 1 : n - 2
t(1:3,1:3) = [ v(1:3,i)'; v(1:3,i+1)'; v(1:3,n)' ]';
area_vector_triangle = triangle_area_vector_3d ( t );
area_vector(1:3,1) = area_vector(1:3,1) + area_vector_triangle(1:3,1);
end
area = 0.5 * sqrt ( sum ( area_vector(1:3).^2 ) );
return
end