forked from Archive/PX4-Autopilot
Matlab tools: Add ellipsoid fit
This commit is contained in:
Lorenz Meier
parent
baca229b95
commit
a4a6e69521
|
|
@ -0,0 +1,174 @@
|
||||||
|
% Copyright (c) 2009, Yury Petrov
|
||||||
|
% All rights reserved.
|
||||||
|
%
|
||||||
|
% Redistribution and use in source and binary forms, with or without
|
||||||
|
% modification, are permitted provided that the following conditions are
|
||||||
|
% met:
|
||||||
|
%
|
||||||
|
% * Redistributions of source code must retain the above copyright
|
||||||
|
% notice, this list of conditions and the following disclaimer.
|
||||||
|
% * 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 OWNER 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.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [ center, radii, evecs, v ] = ellipsoid_fit( X, flag, equals )
|
||||||
|
%
|
||||||
|
% Fit an ellispoid/sphere to a set of xyz data points:
|
||||||
|
%
|
||||||
|
% [center, radii, evecs, pars ] = ellipsoid_fit( X )
|
||||||
|
% [center, radii, evecs, pars ] = ellipsoid_fit( [x y z] );
|
||||||
|
% [center, radii, evecs, pars ] = ellipsoid_fit( X, 1 );
|
||||||
|
% [center, radii, evecs, pars ] = ellipsoid_fit( X, 2, 'xz' );
|
||||||
|
% [center, radii, evecs, pars ] = ellipsoid_fit( X, 3 );
|
||||||
|
%
|
||||||
|
% Parameters:
|
||||||
|
% * X, [x y z] - Cartesian data, n x 3 matrix or three n x 1 vectors
|
||||||
|
% * flag - 0 fits an arbitrary ellipsoid (default),
|
||||||
|
% - 1 fits an ellipsoid with its axes along [x y z] axes
|
||||||
|
% - 2 followed by, say, 'xy' fits as 1 but also x_rad = y_rad
|
||||||
|
% - 3 fits a sphere
|
||||||
|
%
|
||||||
|
% Output:
|
||||||
|
% * center - ellispoid center coordinates [xc; yc; zc]
|
||||||
|
% * ax - ellipsoid radii [a; b; c]
|
||||||
|
% * evecs - ellipsoid radii directions as columns of the 3x3 matrix
|
||||||
|
% * v - the 9 parameters describing the ellipsoid algebraically:
|
||||||
|
% Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz = 1
|
||||||
|
%
|
||||||
|
% Author:
|
||||||
|
% Yury Petrov, Northeastern University, Boston, MA
|
||||||
|
%
|
||||||
|
|
||||||
|
error( nargchk( 1, 3, nargin ) ); % check input arguments
|
||||||
|
if nargin == 1
|
||||||
|
flag = 0; % default to a free ellipsoid
|
||||||
|
end
|
||||||
|
if flag == 2 && nargin == 2
|
||||||
|
equals = 'xy';
|
||||||
|
end
|
||||||
|
|
||||||
|
if size( X, 2 ) ~= 3
|
||||||
|
error( 'Input data must have three columns!' );
|
||||||
|
else
|
||||||
|
x = X( :, 1 );
|
||||||
|
y = X( :, 2 );
|
||||||
|
z = X( :, 3 );
|
||||||
|
end
|
||||||
|
|
||||||
|
% need nine or more data points
|
||||||
|
if length( x ) < 9 && flag == 0
|
||||||
|
error( 'Must have at least 9 points to fit a unique ellipsoid' );
|
||||||
|
end
|
||||||
|
if length( x ) < 6 && flag == 1
|
||||||
|
error( 'Must have at least 6 points to fit a unique oriented ellipsoid' );
|
||||||
|
end
|
||||||
|
if length( x ) < 5 && flag == 2
|
||||||
|
error( 'Must have at least 5 points to fit a unique oriented ellipsoid with two axes equal' );
|
||||||
|
end
|
||||||
|
if length( x ) < 3 && flag == 3
|
||||||
|
error( 'Must have at least 4 points to fit a unique sphere' );
|
||||||
|
end
|
||||||
|
|
||||||
|
if flag == 0
|
||||||
|
% fit ellipsoid in the form Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz = 1
|
||||||
|
D = [ x .* x, ...
|
||||||
|
y .* y, ...
|
||||||
|
z .* z, ...
|
||||||
|
2 * x .* y, ...
|
||||||
|
2 * x .* z, ...
|
||||||
|
2 * y .* z, ...
|
||||||
|
2 * x, ...
|
||||||
|
2 * y, ...
|
||||||
|
2 * z ]; % ndatapoints x 9 ellipsoid parameters
|
||||||
|
elseif flag == 1
|
||||||
|
% fit ellipsoid in the form Ax^2 + By^2 + Cz^2 + 2Gx + 2Hy + 2Iz = 1
|
||||||
|
D = [ x .* x, ...
|
||||||
|
y .* y, ...
|
||||||
|
z .* z, ...
|
||||||
|
2 * x, ...
|
||||||
|
2 * y, ...
|
||||||
|
2 * z ]; % ndatapoints x 6 ellipsoid parameters
|
||||||
|
elseif flag == 2
|
||||||
|
% fit ellipsoid in the form Ax^2 + By^2 + Cz^2 + 2Gx + 2Hy + 2Iz = 1,
|
||||||
|
% where A = B or B = C or A = C
|
||||||
|
if strcmp( equals, 'yz' ) || strcmp( equals, 'zy' )
|
||||||
|
D = [ y .* y + z .* z, ...
|
||||||
|
x .* x, ...
|
||||||
|
2 * x, ...
|
||||||
|
2 * y, ...
|
||||||
|
2 * z ];
|
||||||
|
elseif strcmp( equals, 'xz' ) || strcmp( equals, 'zx' )
|
||||||
|
D = [ x .* x + z .* z, ...
|
||||||
|
y .* y, ...
|
||||||
|
2 * x, ...
|
||||||
|
2 * y, ...
|
||||||
|
2 * z ];
|
||||||
|
else
|
||||||
|
D = [ x .* x + y .* y, ...
|
||||||
|
z .* z, ...
|
||||||
|
2 * x, ...
|
||||||
|
2 * y, ...
|
||||||
|
2 * z ];
|
||||||
|
end
|
||||||
|
else
|
||||||
|
% fit sphere in the form A(x^2 + y^2 + z^2) + 2Gx + 2Hy + 2Iz = 1
|
||||||
|
D = [ x .* x + y .* y + z .* z, ...
|
||||||
|
2 * x, ...
|
||||||
|
2 * y, ...
|
||||||
|
2 * z ]; % ndatapoints x 4 sphere parameters
|
||||||
|
end
|
||||||
|
|
||||||
|
% solve the normal system of equations
|
||||||
|
v = ( D' * D ) \ ( D' * ones( size( x, 1 ), 1 ) );
|
||||||
|
|
||||||
|
% find the ellipsoid parameters
|
||||||
|
if flag == 0
|
||||||
|
% form the algebraic form of the ellipsoid
|
||||||
|
A = [ v(1) v(4) v(5) v(7); ...
|
||||||
|
v(4) v(2) v(6) v(8); ...
|
||||||
|
v(5) v(6) v(3) v(9); ...
|
||||||
|
v(7) v(8) v(9) -1 ];
|
||||||
|
% find the center of the ellipsoid
|
||||||
|
center = -A( 1:3, 1:3 ) \ [ v(7); v(8); v(9) ];
|
||||||
|
% form the corresponding translation matrix
|
||||||
|
T = eye( 4 );
|
||||||
|
T( 4, 1:3 ) = center';
|
||||||
|
% translate to the center
|
||||||
|
R = T * A * T';
|
||||||
|
% solve the eigenproblem
|
||||||
|
[ evecs evals ] = eig( R( 1:3, 1:3 ) / -R( 4, 4 ) );
|
||||||
|
radii = sqrt( 1 ./ diag( evals ) );
|
||||||
|
else
|
||||||
|
if flag == 1
|
||||||
|
v = [ v(1) v(2) v(3) 0 0 0 v(4) v(5) v(6) ];
|
||||||
|
elseif flag == 2
|
||||||
|
if strcmp( equals, 'xz' ) || strcmp( equals, 'zx' )
|
||||||
|
v = [ v(1) v(2) v(1) 0 0 0 v(3) v(4) v(5) ];
|
||||||
|
elseif strcmp( equals, 'yz' ) || strcmp( equals, 'zy' )
|
||||||
|
v = [ v(2) v(1) v(1) 0 0 0 v(3) v(4) v(5) ];
|
||||||
|
else % xy
|
||||||
|
v = [ v(1) v(1) v(2) 0 0 0 v(3) v(4) v(5) ];
|
||||||
|
end
|
||||||
|
else
|
||||||
|
v = [ v(1) v(1) v(1) 0 0 0 v(2) v(3) v(4) ];
|
||||||
|
end
|
||||||
|
center = ( -v( 7:9 ) ./ v( 1:3 ) )';
|
||||||
|
gam = 1 + ( v(7)^2 / v(1) + v(8)^2 / v(2) + v(9)^2 / v(3) );
|
||||||
|
radii = ( sqrt( gam ./ v( 1:3 ) ) )';
|
||||||
|
evecs = eye( 3 );
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -1,6 +1,19 @@
|
||||||
%
|
%
|
||||||
% Tool for plotting mag data
|
% Tool for plotting mag data
|
||||||
%
|
%
|
||||||
|
% Reference values:
|
||||||
|
% telem> [cal] mag #0 off: x:0.15 y:0.07 z:0.14 Ga
|
||||||
|
% MATLAB: x:0.1581 y: 0.0701 z: 0.1439 Ga
|
||||||
|
% telem> [cal] mag #0 scale: x:1.10 y:0.97 z:1.02
|
||||||
|
% MATLAB: 0.5499, 0.5190, 0.4907
|
||||||
|
%
|
||||||
|
% telem> [cal] mag #1 off: x:-0.18 y:0.11 z:-0.09 Ga
|
||||||
|
% MATLAB: x:-0.1827 y:0.1147 z:-0.0848 Ga
|
||||||
|
% telem> [cal] mag #1 scale: x:1.00 y:1.00 z:1.00
|
||||||
|
% MATLAB: 0.5122, 0.5065, 0.4915
|
||||||
|
%
|
||||||
|
%
|
||||||
|
|
||||||
close all;
|
close all;
|
||||||
clear all;
|
clear all;
|
||||||
|
|
||||||
|
|
@ -13,11 +26,11 @@ ymin = -ymax;
|
||||||
zmax = plot_scale;
|
zmax = plot_scale;
|
||||||
zmin = -zmax;
|
zmin = -zmax;
|
||||||
|
|
||||||
mag0_raw = load('../../mag0_raw.csv');
|
mag0_raw = load('../../mag0_raw2.csv');
|
||||||
mag1_raw = load('../../mag1_raw.csv');
|
mag1_raw = load('../../mag1_raw2.csv');
|
||||||
|
|
||||||
mag0_cal = load('../../mag0_cal.csv');
|
mag0_cal = load('../../mag0_cal2.csv');
|
||||||
mag1_cal = load('../../mag1_cal.csv');
|
mag1_cal = load('../../mag1_cal2.csv');
|
||||||
|
|
||||||
fm0r = figure();
|
fm0r = figure();
|
||||||
|
|
||||||
|
|
@ -25,15 +38,21 @@ mag0_x_scale = 1.07;
|
||||||
mag0_y_scale = 0.95;
|
mag0_y_scale = 0.95;
|
||||||
mag0_z_scale = 1.00;
|
mag0_z_scale = 1.00;
|
||||||
|
|
||||||
plot3(mag0_raw(:,1) .* mag0_x_scale, mag0_raw(:,2) .* mag0_y_scale, mag0_raw(:,3) .* mag0_z_scale, '*r');
|
plot3(mag0_raw(:,1), mag0_raw(:,2), mag0_raw(:,3), '*r');
|
||||||
|
[center, radii, evecs, pars ] = ellipsoid_fit( [mag0_raw(:,1) mag0_raw(:,2) mag0_raw(:,3)] );
|
||||||
|
center
|
||||||
|
radii
|
||||||
axis([xmin xmax ymin ymax zmin zmax])
|
axis([xmin xmax ymin ymax zmin zmax])
|
||||||
|
|
||||||
fm1r = figure();
|
fm1r = figure();
|
||||||
plot3(mag1_raw(:,1), mag1_raw(:,2), mag1_raw(:,3), '*r');
|
plot3(mag1_raw(:,1), mag1_raw(:,2), mag1_raw(:,3), '*r');
|
||||||
|
[center, radii, evecs, pars ] = ellipsoid_fit( [mag1_raw(:,1) mag1_raw(:,2) mag1_raw(:,3)] );
|
||||||
|
center
|
||||||
|
radii
|
||||||
axis([xmin xmax ymin ymax zmin zmax])
|
axis([xmin xmax ymin ymax zmin zmax])
|
||||||
|
|
||||||
fm0c = figure();
|
fm0c = figure();
|
||||||
plot3(mag0_cal(:,1), mag0_cal(:,2), mag0_cal(:,3), '*b');
|
plot3(mag0_cal(:,1) .* mag0_x_scale, mag0_cal(:,2) .* mag0_y_scale, mag0_cal(:,3) .* mag0_z_scale, '*b');
|
||||||
axis([xmin xmax ymin ymax zmin zmax])
|
axis([xmin xmax ymin ymax zmin zmax])
|
||||||
|
|
||||||
fm1c = figure();
|
fm1c = figure();
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue