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## Copyright (C) 1999-2022 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
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########################################################################

## -*- texinfo -*-
## @deftypefn  {} {} polyarea (@var{x}, @var{y})
## @deftypefnx {} {} 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 .* (shift (y, -1) - shift (y, 1)))) / 2;
  else
    a = abs (sum (x .* (shift (y, -1, dim) - shift (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)