--- /dev/null
+%% Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% This program is free software; you can redistribute it and/or modify
+%% it under the terms of the GNU General Public License as published by
+%% the Free Software Foundation; either version 3 of the License, or
+%% (at your option) any later version.
+%%
+%% This program is distributed in the hope that it will be useful,
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+%% GNU General Public License for more details.
+%%
+%% You should have received a copy of the GNU General Public License
+%% along with this program; if not, see <http://www.gnu.org/licenses/>.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} { @var{a} =} shapearea (@var{pp})
+%% Calculate the area of a 2D shape defined with piecewise smooth polynomials.
+%%
+%% Shape is defined with piecewise smooth polynomials. @var{pp} is a
+%% cell where each elements is a 2-by-(poly_degree+1) array containing a pair of
+%% polynomials.
+%%
+%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
+%%
+%% @seealso{shapecentroid, shape2polygon, shapeplot}
+%% @end deftypefn
+
+function [A ccw] = shapearea (shape)
+
+ A = sum(cellfun (@Aint, shape));
+ if A < 0
+ warning ('geom2d:shapearea:InvalidResult', ...
+ 'Shape has negative area. Assuming this is due to a clockwise parametrization of the boundary');
+ A = -A;
+ end
+
+endfunction
+
+function dA = Aint (x)
+
+ px = x(1,:);
+ py = x(2,:);
+
+ P = polyint (conv (px, polyder(py)));
+
+ dA = diff(polyval(P,[0 1]));
+
+end
+
+%!demo % non-convex piece-wise polynomial shape
+%! boomerang = {[ 0 -2 1; ...
+%! -4 4 0]; ...
+%! [0.25 -1; ...
+%! 0 0]; ...
+%! [ 0 1.5 -0.75; ...
+%! -3 3 0];
+%! [0.25 0.75; ...
+%! 0 0]};
+%! A = shapearea (boomerang)
+
+%!test
+%! triangle = {[1 0; 0 0]; [-0.5 1; 1 0]; [-0.5 0.5; -1 1]};
+%! A = shapearea (triangle);
+%! assert (0.5, A);
+
+%!test
+%! circle = {[1.715729 -6.715729 0 5; ...
+%! -1.715729 -1.568542 8.284271 0]; ...
+%! [1.715729 1.568542 -8.284271 0; ...
+%! 1.715729 -6.715729 0 5]; ...
+%! [-1.715729 6.715729 0 -5; ...
+%! 1.715729 1.568542 -8.284271 0]; ...
+%! [-1.715729 -1.568542 8.284271 0; ...
+%! -1.715729 6.715729 0 -5]};
+%! A = shapearea (circle);
+%! assert (pi*5^2, A, 5e-2);