%% 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);
