pointSetPrincipalDir

Below is a demonstration of the features of the pointSetPrincipalDir function

Contents

clear; close all; clc;

Syntax

[V,S,U]=pointSetPrincipalDir(X)

Description

Examples

Plot settings

fontSize=15;
markerSize=25;

Using pointSetPrincipalDir to determine main directions of a point cloud

Simulating an ellipsoid with known directions

% Ellipsoid axis stretch factors
ellipStretchTrue=[pi 2 1]

% Create ellipsoid patch data
[F,V,~]=geoSphere(3,1);

V=V.*ellipStretchTrue(ones(size(V,1),1),:);

%Create Euler angles to set directions
E=[-0.25*pi 0.25*pi 0.25*pi];
[R_true,~]=euler2DCM(E); %The true directions for X, Y and Z axis
V=(R_true*V')'; %Rotate polyhedron
ellipStretchTrue =

    3.1416    2.0000    1.0000

This is the true axis system

R_true
R_true =

    0.5000   -0.5000    0.7071
    0.1464    0.8536    0.5000
   -0.8536   -0.1464    0.5000

Determine principal directions of the point set (in this case an ellipsoidal polyhedron).

[R_fit]=pointSetPrincipalDir(V)
R_fit =

    0.5000   -0.5000    0.7071
    0.1464    0.8536    0.5000
   -0.8536   -0.1464    0.5000

Visualizing results

cFigure; hold on;
gtitle('The polyhedron with true (transparant) and determined (solid) axis directions',fontSize);
gpatch(F,V,0.75*ones(1,3),'none',0.5);
plotV(V,'k.','MarkerSize',markerSize);
hl1=quiverTriad(mean(V,1),R_true,10,[],0.2);
hl2=quiverTriad(mean(V,1),R_fit,7,[],1);
legend([hl1 hl2],{'True directions','Fitted directions'});
camlight('headlight');
axisGeom(gca,fontSize);
drawnow;

Output of the singular value decomposition data data

[R_fit,S,U]=pointSetPrincipalDir(V)
R_fit =

    0.5000   -0.5000    0.7071
    0.1464    0.8536    0.5000
   -0.8536   -0.1464    0.5000


S =

   45.9575         0         0
         0   29.2575         0
         0         0   14.6287


U =

    0.0000   -0.0359   -0.0581
   -0.0000   -0.0359    0.0581
    0.0000    0.0359    0.0581
   -0.0000    0.0359   -0.0581
   -0.0359   -0.0581   -0.0000
   -0.0359    0.0581    0.0000
    0.0359    0.0581    0.0000
    0.0359   -0.0581   -0.0000
   -0.0581    0.0000   -0.0359
    0.0581    0.0000   -0.0359
    0.0581   -0.0000    0.0359
   -0.0581   -0.0000    0.0359
    0.0000    0.0000   -0.0684
   -0.0211   -0.0553   -0.0342
    0.0211   -0.0553   -0.0342
   -0.0342   -0.0211   -0.0553
    0.0342   -0.0211   -0.0553
    0.0000   -0.0000    0.0684
   -0.0211   -0.0553    0.0342
    0.0211   -0.0553    0.0342
    0.0342   -0.0211    0.0553
   -0.0342   -0.0211    0.0553
   -0.0211    0.0553    0.0342
    0.0211    0.0553    0.0342
    0.0342    0.0211    0.0553
   -0.0342    0.0211    0.0553
   -0.0211    0.0553   -0.0342
    0.0211    0.0553   -0.0342
   -0.0342    0.0211   -0.0553
    0.0342    0.0211   -0.0553
   -0.0000   -0.0684   -0.0000
   -0.0553   -0.0342   -0.0211
   -0.0553   -0.0342    0.0211
   -0.0000    0.0684    0.0000
   -0.0553    0.0342   -0.0211
   -0.0553    0.0342    0.0211
    0.0553    0.0342   -0.0211
    0.0553    0.0342    0.0211
    0.0553   -0.0342   -0.0211
    0.0553   -0.0342    0.0211
   -0.0684    0.0000   -0.0000
    0.0684   -0.0000    0.0000
    0.0000   -0.0187   -0.0658
   -0.0110   -0.0474   -0.0480
    0.0110   -0.0474   -0.0480
   -0.0178   -0.0297   -0.0590
    0.0178   -0.0297   -0.0590
    0.0000   -0.0187    0.0658
   -0.0110   -0.0474    0.0480
    0.0110   -0.0474    0.0480
    0.0178   -0.0297    0.0590
   -0.0178   -0.0297    0.0590
    0.0000    0.0187    0.0658
   -0.0110    0.0474    0.0480
    0.0110    0.0474    0.0480
    0.0178    0.0297    0.0590
   -0.0178    0.0297    0.0590
   -0.0000    0.0187   -0.0658
   -0.0110    0.0474   -0.0480
    0.0110    0.0474   -0.0480
   -0.0178    0.0297   -0.0590
    0.0178    0.0297   -0.0590
   -0.0297   -0.0590   -0.0178
   -0.0297   -0.0590    0.0178
   -0.0187   -0.0658   -0.0000
   -0.0474   -0.0480   -0.0110
   -0.0474   -0.0480    0.0110
   -0.0297    0.0590    0.0178
   -0.0297    0.0590   -0.0178
   -0.0187    0.0658    0.0000
   -0.0474    0.0480   -0.0110
   -0.0474    0.0480    0.0110
    0.0297    0.0590    0.0178
    0.0297    0.0590   -0.0178
    0.0187    0.0658    0.0000
    0.0474    0.0480   -0.0110
    0.0474    0.0480    0.0110
    0.0297   -0.0590   -0.0178
    0.0297   -0.0590    0.0178
    0.0187   -0.0658   -0.0000
    0.0474   -0.0480   -0.0110
    0.0474   -0.0480    0.0110
   -0.0480   -0.0110   -0.0474
   -0.0480    0.0110   -0.0474
   -0.0590   -0.0178   -0.0297
   -0.0590    0.0178   -0.0297
   -0.0658    0.0000   -0.0187
    0.0480   -0.0110   -0.0474
    0.0480    0.0110   -0.0474
    0.0590    0.0178   -0.0297
    0.0590   -0.0178   -0.0297
    0.0658   -0.0000   -0.0187
    0.0480   -0.0110    0.0474
    0.0480    0.0110    0.0474
    0.0590    0.0178    0.0297
    0.0590   -0.0178    0.0297
    0.0658   -0.0000    0.0187
   -0.0480   -0.0110    0.0474
   -0.0480    0.0110    0.0474
   -0.0590   -0.0178    0.0297
   -0.0590    0.0178    0.0297
   -0.0658    0.0000    0.0187
   -0.0180   -0.0111   -0.0650
    0.0180   -0.0111   -0.0650
   -0.0180    0.0111   -0.0650
    0.0180    0.0111   -0.0650
   -0.0000   -0.0581   -0.0359
   -0.0291   -0.0402   -0.0470
   -0.0111   -0.0650   -0.0180
   -0.0402   -0.0470   -0.0291
    0.0291   -0.0402   -0.0470
    0.0111   -0.0650   -0.0180
    0.0402   -0.0470   -0.0291
   -0.0359    0.0000   -0.0581
   -0.0470   -0.0291   -0.0402
    0.0359    0.0000   -0.0581
    0.0470   -0.0291   -0.0402
    0.0180   -0.0111    0.0650
   -0.0180   -0.0111    0.0650
    0.0180    0.0111    0.0650
   -0.0180    0.0111    0.0650
    0.0000   -0.0581    0.0359
   -0.0291   -0.0402    0.0470
   -0.0111   -0.0650    0.0180
   -0.0402   -0.0470    0.0291
    0.0291   -0.0402    0.0470
    0.0111   -0.0650    0.0180
    0.0402   -0.0470    0.0291
    0.0359   -0.0000    0.0581
    0.0470   -0.0291    0.0402
   -0.0359   -0.0000    0.0581
   -0.0470   -0.0291    0.0402
    0.0000    0.0581    0.0359
   -0.0291    0.0402    0.0470
   -0.0111    0.0650    0.0180
   -0.0402    0.0470    0.0291
    0.0291    0.0402    0.0470
    0.0111    0.0650    0.0180
    0.0402    0.0470    0.0291
    0.0470    0.0291    0.0402
   -0.0470    0.0291    0.0402
   -0.0000    0.0581   -0.0359
   -0.0291    0.0402   -0.0470
   -0.0111    0.0650   -0.0180
   -0.0402    0.0470   -0.0291
    0.0291    0.0402   -0.0470
    0.0111    0.0650   -0.0180
    0.0402    0.0470   -0.0291
   -0.0470    0.0291   -0.0402
    0.0470    0.0291   -0.0402
   -0.0581   -0.0359    0.0000
   -0.0650   -0.0180   -0.0111
   -0.0650   -0.0180    0.0111
   -0.0581    0.0359   -0.0000
   -0.0650    0.0180   -0.0111
   -0.0650    0.0180    0.0111
    0.0581    0.0359    0.0000
    0.0650    0.0180   -0.0111
    0.0650    0.0180    0.0111
    0.0581   -0.0359    0.0000
    0.0650   -0.0180   -0.0111
    0.0650   -0.0180    0.0111
   -0.0000   -0.0276   -0.0626
   -0.0055   -0.0421   -0.0536
    0.0055   -0.0421   -0.0536
   -0.0090   -0.0331   -0.0591
    0.0090   -0.0331   -0.0591
    0.0000   -0.0276    0.0626
   -0.0055   -0.0421    0.0536
    0.0055   -0.0421    0.0536
    0.0090   -0.0331    0.0591
   -0.0090   -0.0331    0.0591
    0.0000    0.0276    0.0626
   -0.0055    0.0421    0.0536
    0.0055    0.0421    0.0536
    0.0090    0.0331    0.0591
   -0.0090    0.0331    0.0591
    0.0000    0.0276   -0.0626
   -0.0055    0.0421   -0.0536
    0.0055    0.0421   -0.0536
   -0.0090    0.0331   -0.0591
    0.0090    0.0331   -0.0591
   -0.0331   -0.0591   -0.0090
   -0.0331   -0.0591    0.0090
   -0.0276   -0.0626   -0.0000
   -0.0421   -0.0536   -0.0055
   -0.0421   -0.0536    0.0055
   -0.0331    0.0591    0.0090
   -0.0331    0.0591   -0.0090
   -0.0276    0.0626    0.0000
   -0.0421    0.0536   -0.0055
   -0.0421    0.0536    0.0055
    0.0331    0.0591    0.0090
    0.0331    0.0591   -0.0090
    0.0276    0.0626    0.0000
    0.0421    0.0536   -0.0055
    0.0421    0.0536    0.0055
    0.0331   -0.0591   -0.0090
    0.0331   -0.0591    0.0090
    0.0276   -0.0626   -0.0000
    0.0421   -0.0536   -0.0055
    0.0421   -0.0536    0.0055
   -0.0536   -0.0055   -0.0421
   -0.0536    0.0055   -0.0421
   -0.0591   -0.0090   -0.0331
   -0.0591    0.0090   -0.0331
   -0.0626    0.0000   -0.0276
    0.0536   -0.0055   -0.0421
    0.0536    0.0055   -0.0421
    0.0591    0.0090   -0.0331
    0.0591   -0.0090   -0.0331
    0.0626    0.0000   -0.0276
    0.0536   -0.0055    0.0421
    0.0536    0.0055    0.0421
    0.0591    0.0090    0.0331
    0.0591   -0.0090    0.0331
    0.0626   -0.0000    0.0276
   -0.0536   -0.0055    0.0421
   -0.0536    0.0055    0.0421
   -0.0591   -0.0090    0.0331
   -0.0591    0.0090    0.0331
   -0.0626   -0.0000    0.0276
   -0.0000   -0.0094   -0.0677
    0.0000    0.0094   -0.0677
   -0.0091   -0.0056   -0.0675
    0.0091   -0.0056   -0.0675
   -0.0091    0.0056   -0.0675
    0.0091    0.0056   -0.0675
   -0.0162   -0.0519   -0.0415
   -0.0256   -0.0577   -0.0262
   -0.0107   -0.0574   -0.0355
   -0.0254   -0.0483   -0.0411
   -0.0163   -0.0609   -0.0264
   -0.0310   -0.0518   -0.0320
    0.0162   -0.0519   -0.0415
    0.0256   -0.0577   -0.0262
    0.0107   -0.0574   -0.0355
    0.0254   -0.0483   -0.0411
    0.0163   -0.0609   -0.0264
    0.0310   -0.0518   -0.0320
   -0.0262   -0.0256   -0.0577
   -0.0415   -0.0162   -0.0519
   -0.0264   -0.0163   -0.0609
   -0.0320   -0.0310   -0.0518
   -0.0355   -0.0107   -0.0574
   -0.0411   -0.0254   -0.0483
    0.0262   -0.0256   -0.0577
    0.0415   -0.0162   -0.0519
    0.0264   -0.0163   -0.0609
    0.0320   -0.0310   -0.0518
    0.0355   -0.0107   -0.0574
    0.0411   -0.0254   -0.0483
    0.0000   -0.0094    0.0677
    0.0000    0.0094    0.0677
    0.0091   -0.0056    0.0675
   -0.0091   -0.0056    0.0675
    0.0091    0.0056    0.0675
   -0.0091    0.0056    0.0675
   -0.0162   -0.0519    0.0415
   -0.0256   -0.0577    0.0262
   -0.0107   -0.0574    0.0355
   -0.0254   -0.0483    0.0411
   -0.0163   -0.0609    0.0264
   -0.0310   -0.0518    0.0320
    0.0162   -0.0519    0.0415
    0.0256   -0.0577    0.0262
    0.0107   -0.0574    0.0355
    0.0254   -0.0483    0.0411
    0.0163   -0.0609    0.0264
    0.0310   -0.0518    0.0320
    0.0262   -0.0256    0.0577
    0.0415   -0.0162    0.0519
    0.0264   -0.0163    0.0609
    0.0320   -0.0310    0.0518
    0.0355   -0.0107    0.0574
    0.0411   -0.0254    0.0483
   -0.0262   -0.0256    0.0577
   -0.0415   -0.0162    0.0519
   -0.0264   -0.0163    0.0609
   -0.0320   -0.0310    0.0518
   -0.0355   -0.0107    0.0574
   -0.0411   -0.0254    0.0483
   -0.0162    0.0519    0.0415
   -0.0256    0.0577    0.0262
   -0.0107    0.0574    0.0355
   -0.0254    0.0483    0.0411
   -0.0163    0.0609    0.0264
   -0.0310    0.0518    0.0320
    0.0162    0.0519    0.0415
    0.0256    0.0577    0.0262
    0.0107    0.0574    0.0355
    0.0254    0.0483    0.0411
    0.0163    0.0609    0.0264
    0.0310    0.0518    0.0320
    0.0262    0.0256    0.0577
    0.0415    0.0162    0.0519
    0.0264    0.0163    0.0609
    0.0355    0.0107    0.0574
    0.0320    0.0310    0.0518
    0.0411    0.0254    0.0483
   -0.0262    0.0256    0.0577
   -0.0415    0.0162    0.0519
   -0.0264    0.0163    0.0609
   -0.0355    0.0107    0.0574
   -0.0320    0.0310    0.0518
   -0.0411    0.0254    0.0483
   -0.0162    0.0519   -0.0415
   -0.0256    0.0577   -0.0262
   -0.0107    0.0574   -0.0355
   -0.0254    0.0483   -0.0411
   -0.0163    0.0609   -0.0264
   -0.0310    0.0518   -0.0320
    0.0162    0.0519   -0.0415
    0.0256    0.0577   -0.0262
    0.0107    0.0574   -0.0355
    0.0254    0.0483   -0.0411
    0.0163    0.0609   -0.0264
    0.0310    0.0518   -0.0320
   -0.0262    0.0256   -0.0577
   -0.0415    0.0162   -0.0519
   -0.0264    0.0163   -0.0609
   -0.0355    0.0107   -0.0574
   -0.0320    0.0310   -0.0518
   -0.0411    0.0254   -0.0483
    0.0262    0.0256   -0.0577
    0.0415    0.0162   -0.0519
    0.0264    0.0163   -0.0609
    0.0355    0.0107   -0.0574
    0.0320    0.0310   -0.0518
    0.0411    0.0254   -0.0483
   -0.0094   -0.0677   -0.0000
    0.0094   -0.0677    0.0000
   -0.0056   -0.0675   -0.0091
    0.0056   -0.0675   -0.0091
   -0.0056   -0.0675    0.0091
    0.0056   -0.0675    0.0091
   -0.0519   -0.0415   -0.0162
   -0.0577   -0.0262   -0.0256
   -0.0483   -0.0411   -0.0254
   -0.0518   -0.0320   -0.0310
   -0.0574   -0.0355   -0.0107
   -0.0609   -0.0264   -0.0163
   -0.0519   -0.0415    0.0162
   -0.0577   -0.0262    0.0256
   -0.0483   -0.0411    0.0254
   -0.0518   -0.0320    0.0310
   -0.0574   -0.0355    0.0107
   -0.0609   -0.0264    0.0163
   -0.0094    0.0677    0.0000
    0.0094    0.0677    0.0000
   -0.0056    0.0675    0.0091
    0.0056    0.0675    0.0091
   -0.0056    0.0675   -0.0091
    0.0056    0.0675   -0.0091
   -0.0519    0.0415   -0.0162
   -0.0577    0.0262   -0.0256
   -0.0483    0.0411   -0.0254
   -0.0518    0.0320   -0.0310
   -0.0574    0.0355   -0.0107
   -0.0609    0.0264   -0.0163
   -0.0519    0.0415    0.0162
   -0.0577    0.0262    0.0256
   -0.0483    0.0411    0.0254
   -0.0518    0.0320    0.0310
   -0.0574    0.0355    0.0107
   -0.0609    0.0264    0.0163
    0.0519    0.0415   -0.0162
    0.0577    0.0262   -0.0256
    0.0483    0.0411   -0.0254
    0.0518    0.0320   -0.0310
    0.0574    0.0355   -0.0107
    0.0609    0.0264   -0.0163
    0.0519    0.0415    0.0162
    0.0577    0.0262    0.0256
    0.0483    0.0411    0.0254
    0.0518    0.0320    0.0310
    0.0574    0.0355    0.0107
    0.0609    0.0264    0.0163
    0.0519   -0.0415   -0.0162
    0.0577   -0.0262   -0.0256
    0.0483   -0.0411   -0.0254
    0.0518   -0.0320   -0.0310
    0.0574   -0.0355   -0.0107
    0.0609   -0.0264   -0.0163
    0.0519   -0.0415    0.0162
    0.0577   -0.0262    0.0256
    0.0483   -0.0411    0.0254
    0.0518   -0.0320    0.0310
    0.0574   -0.0355    0.0107
    0.0609   -0.0264    0.0163
   -0.0677    0.0000   -0.0094
   -0.0677    0.0000    0.0094
   -0.0675   -0.0091   -0.0056
   -0.0675   -0.0091    0.0056
   -0.0675    0.0091   -0.0056
   -0.0675    0.0091    0.0056
    0.0677   -0.0000   -0.0094
    0.0677   -0.0000    0.0094
    0.0675    0.0091   -0.0056
    0.0675    0.0091    0.0056
    0.0675   -0.0091   -0.0056
    0.0675   -0.0091    0.0056
   -0.0090   -0.0245   -0.0632
    0.0090   -0.0245   -0.0632
   -0.0091   -0.0150   -0.0661
    0.0091   -0.0150   -0.0661
   -0.0000   -0.0480   -0.0486
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GIBBON www.gibboncode.org

Kevin Mattheus Moerman, gibbon.toolbox@gmail.com

GIBBON footer text

License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2019 Kevin Mattheus Moerman

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/.