/usr/share/octave/packages/geometry-1.7.0/shape2d/shapearea.m is in octave-geometry 1.7.0-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | ## Copyright (C) 2012 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);
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