Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / inertiaEllipse.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/inertiaEllipse.m b/octave_packages/geometry-1.5.0/geom2d/inertiaEllipse.m
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+%% Copyright (c) 2011, INRA
+%% 2008-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% Redistribution and use in source and binary forms, with or without
+%% modification, are permitted provided that the following conditions are met:
+%%
+%% 1. Redistributions of source code must retain the above copyright notice, this
+%%    list of conditions and the following disclaimer.
+%%     
+%% 2. Redistributions in binary form must reproduce the above copyright notice, 
+%%    this list of conditions and the following disclaimer in the documentation
+%%    and/or other materials provided with the distribution.
+%%
+%% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+%% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+%% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+%% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+%% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
+%% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+%% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
+%% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+%% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+%% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+%% POSSIBILITY OF SUCH DAMAGE.
+%%
+%% The views and conclusions contained in the software and documentation are
+%% those of the authors and should not be interpreted as representing official
+%% policies, either expressed or implied, of copyright holder.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{ell} = } inertiaEllipse (@var{pts})
+%% Inertia ellipse of a set of points
+%%
+%%   ELL = inertiaEllipse(PTS);
+%%   where PTS is a N*2 array containing coordinates of N points, computes
+%%   the inertia ellispe of the set of points.
+%%
+%%   The result has the form:
+%%   ELL = [XC YC A B THETA],
+%%   with XC and YC being the center of mass of the point set, A and B are
+%%   the lengths of the inertia ellipse (see below), and THETA is the angle
+%%   of the main inertia axis with the horizontal (counted in degrees
+%%   between 0 and 180). 
+%%   A and B are the standard deviations of the point coordinates when
+%%   ellipse is aligned with the inertia axes.
+%%
+%%   @example
+%%   pts = randn(100, 2);
+%%   pts = transformPoint(pts, createScaling(5, 2));
+%%   pts = transformPoint(pts, createRotation(pi/6));
+%%   pts = transformPoint(pts, createTranslation(3, 4));
+%%   ell = inertiaEllipse(pts);
+%%   figure(1); clf; hold on;
+%%   drawPoint(pts);
+%%   drawEllipse(ell, 'linewidth', 2, 'color', 'r');
+%% @end example
+%%
+%%   @seealso{ellipses2d, drawEllipse}
+%% @end deftypefn
+
+function ell = inertiaEllipse(points)
+
+  % ellipse center
+  xc = mean(points(:,1));
+  yc = mean(points(:,2));
+
+  % recenter points
+  x = points(:,1) - xc;
+  y = points(:,2) - yc;
+
+  % number of points
+  n = size(points, 1);
+
+  % inertia parameters
+  Ixx = sum(x.^2) / n;
+  Iyy = sum(y.^2) / n;
+  Ixy = sum(x.*y) / n;
+
+  % compute ellipse semi-axis lengths
+  common = sqrt( (Ixx - Iyy)^2 + 4 * Ixy^2);
+  ra = sqrt(2) * sqrt(Ixx + Iyy + common);
+  rb = sqrt(2) * sqrt(Ixx + Iyy - common);
+
+  % compute ellipse angle in degrees
+  theta = atan2(2 * Ixy, Ixx - Iyy) / 2;
+  theta = rad2deg(theta);
+
+  % create the resulting inertia ellipse
+  ell = [xc yc ra rb theta];
+
+endfunction
+