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1 ## Copyright (C) 1999 David M. Doolin <doolin@ce.berkeley.edu> |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} polyarea (@var{x}, @var{y}) |
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22 ## @deftypefnx {Function File} {} polyarea (@var{x}, @var{y}, @var{dim}) |
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23 ## |
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24 ## Determines area of a polygon by triangle method. The variables |
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25 ## @var{x} and @var{y} define the vertex pairs, and must therefore have |
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26 ## the same shape. Then might be either vectors or arrays. If they are |
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27 ## arrays then the columns of @var{x} and @var{y} are treated seperately |
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28 ## and an area returned for each. |
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29 ## |
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30 ## If the optional @var{dim} argument is given, then @code{polyarea} |
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31 ## works along this dimension of the arrays @var{x} and @var{y}. |
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32 ## |
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33 ## @end deftypefn |
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34 |
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35 ## todo: Add moments for centroid, etc. |
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36 ## |
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37 ## bugs and limitations: |
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38 ## Probably ought to be an optional check to make sure that |
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39 ## traversing the vertices doesn't make any sides cross |
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40 ## (Is simple closed curve the technical definition of this?). |
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41 |
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42 ## Author: David M. Doolin <doolin@ce.berkeley.edu> |
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43 ## Date: 1999-04-14 |
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44 ## Modified-by: |
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45 ## 2000-01-15 Paul Kienzle <pkienzle@kienzle.powernet.co.uk> |
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46 ## * use matlab compatible interface |
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47 ## * return absolute value of area so traversal order doesn't matter |
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48 ## 2005-10-13 Torsten Finke |
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49 ## * optimization saving half the sums and multiplies |
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50 |
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51 function a = polyarea (x, y, dim) |
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52 if (nargin != 2 && nargin != 3) |
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53 print_usage (); |
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54 elseif (ndims (x) == ndims (y) && size (x) == size (y)) |
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55 if (nargin == 2) |
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56 a = abs (sum (x .* (shift (y, -1) - shift (y, 1)))) / 2; |
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57 else |
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58 a = abs (sum (x .* (shift (y, -1, dim) - shift (y, 1, dim)), dim)) / 2; |
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59 endif |
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60 else |
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61 error ("polyarea: x and y must have the same shape"); |
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62 endif |
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63 endfunction |
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64 |
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65 %!shared x, y |
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66 %! x = [1;1;3;3;1]; |
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67 %! y = [1;3;3;1;1]; |
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68 %!assert (polyarea(x,y), 4, eps) |
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69 %!assert (polyarea([x,x],[y,y]), [4,4], eps) |
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70 %!assert (polyarea([x,x],[y,y],1), [4,4], eps) |
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71 %!assert (polyarea([x,x]',[y,y]',2), [4;4], eps) |
