/usr/share/octave/packages/geometry-1.7.0/shape2d/shapecentroid.m is in octave-geometry 1.7.0-1build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 | ## Copyright (C) 2012 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,'-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,'-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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