Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / shape2d / shapearea.m

diff --git a/octave_packages/geometry-1.5.0/shape2d/shapearea.m b/octave_packages/geometry-1.5.0/shape2d/shapearea.m
new file mode 100644 (file)
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+++ b/octave_packages/geometry-1.5.0/shape2d/shapearea.m
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+%% 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
+%% (at your option) 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} =} shapearea (@var{pp})
+%% Calculate the area of a 2D shape defined with piecewise smooth polynomials.
+%%
+%% Shape is defined with piecewise smooth polynomials. @var{pp} is a
+%% cell where each elements is a 2-by-(poly_degree+1) array containing a pair of
+%% polynomials.
+%%
+%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
+%%
+%% @seealso{shapecentroid, shape2polygon, shapeplot}
+%% @end deftypefn
+
+function [A ccw] = shapearea (shape)
+
+  A = sum(cellfun (@Aint, shape));
+  if A < 0
+    warning ('geom2d:shapearea:InvalidResult', ...
+    'Shape has negative area. Assuming this is due to a clockwise parametrization of the boundary');
+    A = -A;
+  end
+
+endfunction
+
+function dA = Aint (x)
+
+    px = x(1,:);
+    py = x(2,:);
+
+    P = polyint (conv (px, polyder(py)));
+
+    dA = diff(polyval(P,[0 1]));
+
+end
+
+%!demo % non-convex piece-wise polynomial shape
+%! boomerang = {[ 0 -2 1; ...
+%!               -4  4 0]; ...
+%!              [0.25 -1; ...
+%!               0     0]; ...
+%!              [ 0 1.5 -0.75; ...
+%!               -3 3    0];
+%!              [0.25 0.75; ...
+%!               0 0]};
+%! A = shapearea (boomerang)
+
+%!test
+%! triangle = {[1 0; 0 0]; [-0.5 1; 1 0]; [-0.5 0.5; -1 1]};
+%! A = shapearea (triangle);
+%! assert (0.5, A);
+
+%!test
+%! circle = {[1.715729  -6.715729    0   5; ...
+%!            -1.715729  -1.568542   8.284271    0]; ...
+%!            [1.715729   1.568542  -8.284271    0; ...
+%!             1.715729  -6.715729    0   5]; ...
+%!            [-1.715729   6.715729    0  -5; ...
+%!             1.715729   1.568542  -8.284271    0]; ...
+%!            [-1.715729  -1.568542   8.284271    0; ...
+%!            -1.715729   6.715729    0  -5]};
+%! A = shapearea (circle);
+%! assert (pi*5^2, A, 5e-2);