update packages

[CreaPhase.git] / octave_packages / m / general / polyarea.m

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+## Copyright (C) 1999-2012 David M. Doolin
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} polyarea (@var{x}, @var{y})
+## @deftypefnx {Function File} {} 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
+
+## todo:  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?).
+
+## Author: David M. Doolin <doolin@ce.berkeley.edu>
+## Date: 1999-04-14
+## Modified-by:
+##    2000-01-15 Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
+##    * use matlab compatible interface
+##    * return absolute value of area so traversal order doesn't matter
+##    2005-10-13 Torsten Finke
+##    * optimization saving half the sums and multiplies
+
+function a = polyarea (x, y, dim)
+  if (nargin != 2 && nargin != 3)
+    print_usage ();
+  elseif (size_equal (x, y))
+    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
+  else
+    error ("polyarea: X and Y must have the same shape");
+  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)