1 %% Copyright (c) 2011, INRA
2 %% 2008-2011, David Legland <david.legland@grignon.inra.fr>
3 %% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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35 %% @deftypefn {Function File} {@var{ell} = } inertiaEllipse (@var{pts})
36 %% Inertia ellipse of a set of points
38 %% ELL = inertiaEllipse(PTS);
39 %% where PTS is a N*2 array containing coordinates of N points, computes
40 %% the inertia ellispe of the set of points.
42 %% The result has the form:
43 %% ELL = [XC YC A B THETA],
44 %% with XC and YC being the center of mass of the point set, A and B are
45 %% the lengths of the inertia ellipse (see below), and THETA is the angle
46 %% of the main inertia axis with the horizontal (counted in degrees
47 %% between 0 and 180).
48 %% A and B are the standard deviations of the point coordinates when
49 %% ellipse is aligned with the inertia axes.
52 %% pts = randn(100, 2);
53 %% pts = transformPoint(pts, createScaling(5, 2));
54 %% pts = transformPoint(pts, createRotation(pi/6));
55 %% pts = transformPoint(pts, createTranslation(3, 4));
56 %% ell = inertiaEllipse(pts);
57 %% figure(1); clf; hold on;
59 %% drawEllipse(ell, 'linewidth', 2, 'color', 'r');
62 %% @seealso{ellipses2d, drawEllipse}
65 function ell = inertiaEllipse(points)
68 xc = mean(points(:,1));
69 yc = mean(points(:,2));
83 % compute ellipse semi-axis lengths
84 common = sqrt( (Ixx - Iyy)^2 + 4 * Ixy^2);
85 ra = sqrt(2) * sqrt(Ixx + Iyy + common);
86 rb = sqrt(2) * sqrt(Ixx + Iyy - common);
88 % compute ellipse angle in degrees
89 theta = atan2(2 * Ixy, Ixx - Iyy) / 2;
90 theta = rad2deg(theta);
92 % create the resulting inertia ellipse
93 ell = [xc yc ra rb theta];