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--- a +++ b/inst/area_poly2d.m @@ -0,0 +1,52 @@ +%% Copyright (c) 2011 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 +%% 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} = area_poly2d (@var{p}) +%% Calculates the Area of a 2D polygon. +%% +%% The polygon is described in @var{p}, where each row is a different vertex. +%% The algorithm was adapted from P. Bourke web page +%% @uref{http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/} +%% +%% @seealso{inertia_moment_poly2d, center_mass_poly2d} +%% @end deftypefn + +function A = area_poly2d(poly) + + N = size(poly,1); + nxt = [2:N 1]; + px = poly(:,1); + px_nxt = poly(nxt,1); + py = poly(:,2); + py_nxt = poly(nxt,2); + + A = sum(px.*py_nxt - px_nxt.*py)/2; + +end + +%!demo +%! % A parametrized arbitrary triagle and its area +%! +%! triangle = @(a,b,h) [0 0; b 0; a h]; +%! h = linspace(0.1,1,10); +%! b = pi; +%! for i=1:length(h); +%! P = triangle(0.1,b,h(i)); +%! area(i) = area_poly2d(P); +%! end +%! +%! % The area of the triangle is b*h/2 +%! plot(h,area,'o',h,b*h/2);