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## Copyright (C) 2012-2017 (C) Juan Pablo Carbajal
##
## 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/>.
## Author: Juan Pablo Carbajal <ajuanpi+dev@gmail.com>
## -*- texinfo -*-
## @deftypefn {Function File} { [@var{a}, @var{ccw}]=} 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,:)}.
##
## The returned area is always positive even if the shape is parametrized
## in a clockwise direction. If the case of a clockwise parametrized shape
## @code{@var{ccw} == -1} otherwise @code{@var{ccw} == 1}.
##
## @seealso{shapeCentroid, shape2polygon, plotShape}
## @end deftypefn
function [A ccw] = shapeArea (shape)
A = sum (cellfun (@Aint, shape));
ccw = sign (A);
if (A < 0)
warning ('geom2d:cw-shape', ...
['Shape has negative area. ' ...
'Assuming this is due to a clockwise parametrization of the boundary']);
A = ccw * 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
%! warning('off', 'geom2d:cw-shape', 'local');
%! triangle = {[1 0; 0 0]; [-0.5 1; 1 0]; [-0.5 0.5; -1 1]};
%! A = shapeArea (triangle);
%! assert (0.5, A);
%!test
%! warning('off', 'geom2d:cw-shape', 'local');
%! 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);
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