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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{cm} =} shapecentroid (@var{pp})
%% Centroid of a simple plane shape defined with piecewise smooth polynomials.
%%
%% The shape is defined with piecewise smooth polynomials. @var{pp} is a
%% cell where each elements is a 2-by-(poly_degree+1) matrix containing a pair
%% of polynomials.
%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
%%
%% The edges of the shape should not self-intersect. This function does not check for the
%% sanity of the shape.
%%
%% @seealso{shapearea, shape2polygon}
%% @end deftypefn
function cm = shapecentroid (shape)
cm = sum( cell2mat ( cellfun (@CMint, shape, 'UniformOutput', false)), 1);
A = shapearea(shape);
cm = cm / A;
[~,id] = lastwarn ('','');
if strcmp (id ,'geom2d:shapearea:InvalidResult')
lastwarn('Inverting centroid','geom2d:shapecentroid:InvalidResult');
cm = -cm;
end
endfunction
function dcm = CMint (x)
px = x(1,:);
py = x(2,:);
Px = polyint (conv(conv (-px , py) , polyder (px)));
Py = polyint (conv(conv (px , py) , polyder (py)));
dcm = zeros (1,2);
dcm(1) = diff(polyval(Px,[0 1]));
dcm(2) = diff(polyval(Py,[0 1]));
endfunction
%!demo % non-convex bezier 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]};
%! CoM = shapecentroid (boomerang)
%! Gcentroid = centroid(shape2polygon(boomerang))
%!
%! figure(1); clf;
%! shapeplot(boomerang,10,'-o');
%! hold on
%! drawPoint(CoM,'xk;shape centroid;');
%! drawPoint(Gcentroid,'xr;point centroid;');
%! hold off
%! axis equal
%!demo
%! Lshape = {[0.00000 0.76635; -0.67579 -0.24067]; ...
%! [0.77976 0.76635; 0.00000 -0.91646]; ...
%! [0.00000 1.54611; 0.38614 -0.91646]; ...
%! [-0.43813 1.54611; 0.00000 -0.53032]; ...
%! [0.00000 1.10798; 0.28965 -0.53032]; ...
%! [-0.34163 1.10798; 0.00000 -0.24067]};...
%! CoM = shapecentroid (Lshape)
%! Gcentroid = centroid (shape2polygon (Lshape))
%!
%! shapeplot(Lshape,10,'-o');
%! hold on
%! drawPoint(CoM,'xk;shape centroid;');
%! drawPoint(Gcentroid,'xr;point centroid;');
%! hold off
%! axis equal
%!test
%! square = {[1 -0.5; 0 -0.5]; [0 0.5; 1 -0.5]; [-1 0.5; 0 0.5]; [0 -0.5; -1 0.5]};
%! CoM = shapecentroid (square);
%! assert (CoM, [0 0], sqrt(eps));
%!test
%! square = {[1 -0.5; 0 -0.5]; [0 0.5; 1 -0.5]; [-1 0.5; 0 0.5]; [0 -0.5; -1 0.5]};
%! square_t = shapetransform (square,[1;1]);
%! CoM = shapecentroid (square_t);
%! assert (CoM, [1 1], sqrt(eps));
%!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]};
%! CoM = shapecentroid (circle);
%! assert (CoM , [0 0], 5e-3);
%!shared shape
%! shape = {[-93.172 606.368 -476.054 291.429; ...
%! -431.196 637.253 11.085 163.791]; ...
%! [-75.3626 -253.2337 457.1678 328.5714; ...
%! 438.7659 -653.6278 -7.9953 380.9336]; ...
%! [-89.5841 344.9716 -275.3876 457.1429; ...
%! -170.3613 237.8858 1.0469 158.0765];...
%! [32.900 -298.704 145.804 437.143; ...
%! -243.903 369.597 -34.265 226.648]; ...
%! [-99.081 409.127 -352.903 317.143; ...
%! 55.289 -114.223 -26.781 318.076]; ...
%! [-342.231 191.266 168.108 274.286; ...
%! 58.870 -38.083 -89.358 232.362]};
%!test % x-Reflection
%! v = shapecentroid (shape)(:);
%! T = createLineReflection([0 0 1 0]);
%! nshape = shapetransform (shape, T);
%! vn = shapecentroid (nshape)(:);
%! assert(vn,T(1:2,1:2)*v);
%!test % Rotation
%! v = shapecentroid (shape)(:);
%! T = createRotation(v.',pi/2);
%! nshape = shapetransform (shape, T);
%! vn = shapecentroid (nshape)(:);
%! assert(vn,v,1e-2);
%!test % Translation
%! v = shapecentroid (shape)(:);
%! nshape = shapetransform (shape, -v);
%! vn = shapecentroid (nshape)(:);
%! assert(vn,[0; 0],1e-2);
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