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########################################################################
##
## Copyright (C) 1999-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{a} =} polyarea (@var{x}, @var{y})
## @deftypefnx {} {@var{a} =} polyarea (@var{x}, @var{y}, @var{dim})
##
## Determine area of a polygon by triangle method.
##
## The variables @var{x} and @var{y} define the vertex pairs, and must
## therefore have the same shape. They can be either vectors or arrays. If
## they are arrays then the columns of @var{x} and @var{y} are treated
## separately and an area returned for each.
##
## If the optional @var{dim} argument is given, then @code{polyarea} works
## along this dimension of the arrays @var{x} and @var{y}.
##
## @end deftypefn
## FIXME: Add moments for centroid, etc.
##
## Bugs and limitations:
## Probably ought to be an optional check to make sure that
## traversing the vertices doesn't make any sides cross
## (Is simple closed curve the technical definition of this?).
function a = polyarea (x, y, dim)
if (nargin < 2)
print_usage ();
elseif (! size_equal (x, y))
error ("polyarea: X and Y must have the same shape");
endif
if (nargin == 2)
a = abs (sum (x .* (circshift (y, -1) - circshift (y, 1)))) / 2;
else
a = abs (sum (x .* (circshift (y, -1, dim) - circshift (y, 1, dim)), dim)) / 2;
endif
endfunction
%!shared x, y
%! x = [1;1;3;3;1];
%! y = [1;3;3;1;1];
%!assert (polyarea (x,y), 4, eps)
%!assert (polyarea ([x,x],[y,y]), [4,4], eps)
%!assert (polyarea ([x,x],[y,y],1), [4,4], eps)
%!assert (polyarea ([x,x]',[y,y]',2), [4;4], eps)
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