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%% 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} =} areashape (@var{pp})
%% Shape is defined with piecewise smooth polynomials. @var{pp} is a
%% cell where each elements is a 2-by-(poly_degree+1) array containing px(i,:) =
%% pp{i}(1,:) and py(i,:) = pp{i}(2,:).
%%
%% @end deftypefn
function A = shapearea (pp, tol=sqrt(eps)*[1 1])
A = 0;
integrand = @(t_, px_, py_) polyval (px_, t_) .* polyval ( polyderiv (py_), t_);
d3_integral = @(px,py) py(1) * ( 20*px(4) + 15*px(3) + 12*px(2) + 10*px(1)) / 20 + ...
py(2) * ( 30*px(4) + 20*px(3) + 15*px(2) + 12*px(1)) / 30 + ...
py(3) * ( 12*px(4) + 6*px(3) + 4*px(2) + 3*px(1)) / 12;
for is = 1:numel(pp)
px = pp{is}(1,:);
py = pp{is}(2,:);
if length(px) > 4
% degree> 3
A += quad(@(t) integrand (t, px, py), 0, 1, tol);
else
% cubic polynomial
px = padarray(px,[0 4-length(px)],0,'pre')
py = padarray(py,[0 4-length(py)],0,'pre');
A += d3_integral(px,py);
end
end
endfunction
%!demo % non-convex bezier shape
%! weirdhearth ={[-17.6816 -34.3989 7.8580 3.7971; ...
%! 15.4585 -28.3820 -18.7645 9.8519]; ...
%! [-27.7359 18.1039 -34.5718 3.7878; ...
%! -40.7440 49.7999 -25.5011 2.2304]};
%! A = shapearea (weirdhearth)
%!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);

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