How can the major axis of a 3d object be determined?

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Carson Purnell 2022-6-7

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回答： Carson Purnell 2022-6-15

I have some rodlike objects in 3d, below is an example. Is there a way to find its longitudinal axis? I'm trying to generate a bundle of such objects at different orientations and need to know the axis to be able to rotate them about that axis (and properly place them at the correct distance)

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Answer 1

Carson Purnell 2022-6-15

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Seems like no matlab code has this functionality built in, so I ended up doing it myself. Demo code, assuming you already have a shape within 3d array vol:

%generate points from the volume

[X, Y, Z] = meshgrid(1:size(vol,2), 1:size(vol,1), 1:size(vol,3));

points = [X(:) Y(:) Z(:) vol(:)];

nonzero = points(:,4)>0; %threshold to retain points

filtered = points(nonzero,1:3);

%generate an orientation vector from points

cen = mean(filtered,1);

[~,~,V] = svd((filtered-cen),'econ'); %singular value decomposition, econ for speed

d = V(:,1)'; %the slope vector, ready for input to imrotate3

%demo of line

count =0;

for i=-50:.1:50 %show line

count = count+1;

lin(count,:) = d*i+cen;

end

close all

hold on

plot3(filtered(:,1),filtered(:,2),filtered(:,3),'.')

plot3(lin(:,1),lin(:,2),lin(:,3),'o');

axis equal

function is on the FEX, let me know if it works for anyone else.

https://www.mathworks.com/matlabcentral/fileexchange/113325-shapeaxis-compute-the-axis-orientation-of-3d-shapes

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Answer 2

Kevin Holly 2022-6-9

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编辑：Kevin Holly 2022-6-9

在 MATLAB Online 中打开

You can figure out the orientation with regionprops3 assuming you have a 3D matrix of the model.

Example:

sample = zeros(100,100,100);

sample(5,:,:)=eye(100);

SE = strel("disk", 3);

new_sample=imdilate(sample,SE);

isosurface(new_sample)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

rp = regionprops3(new_sample,'Orientation');

rp.Orientation

ans = 1×3

-90.0000 45.0000 0

Let me rotate it with imrotate3

figure

new_sample_rotated = imrotate3(new_sample,90,rp.Orientation,'nearest','loose','FillValues',0);

isosurface(new_sample_rotated)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

figure

new_sample_rotated = imrotate3(new_sample,35,rp.Orientation,'nearest','loose','FillValues',0);

isosurface(new_sample_rotated)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

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Kevin Holly 2022-6-10

编辑：Kevin Holly 2022-6-10

在 MATLAB Online 中打开

"Euler angles, returned as a 1-by-3 vector. The angles are based on the right-hand rule. regionprops3 interprets the angles by looking at the origin along the x-, y-, and z-axis representing roll, pitch, and yaw respectively. A positive angle represents a rotation in the counterclockwise direction. Rotation operations are not commutative so they must be applied in the correct order to have the intended effect."

sample = zeros(100,100,100);

sample(5,:,:)=eye(100);

SE = strel("disk", 3);

new_sample=imdilate(sample,SE);

isosurface(new_sample)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

rp = regionprops3(new_sample,'Orientation','Centroid');

rp.Orientation

ans = 1×3

-90.0000 45.0000 0

rp.Centroid

ans = 1×3

50.5000 5.0000 50.5000

figure

% new_sample=imtranslate(new_sample,-rp.Centroid);

new_sample_rotated = imrotate3(new_sample,-45,[0 1 0]);

isosurface(new_sample_rotated)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

rp = regionprops3(new_sample_rotated,'Orientation','Centroid');

rp.Orientation

ans = 1×3

90 0 0

rp.Centroid

ans = 1×3

71.5000 5.0000 71.5000

figure

% new_sample_rotated=imtranslate(new_sample,-rp.Centroid);

new_sample_rotated = imrotate3(new_sample_rotated,90,[0 0 1]);

isosurface(new_sample_rotated)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

rp = regionprops3(new_sample_rotated,'Orientation');

rp.Orientation

ans = 1×3

0 0 0

Using rotate:

figure

isosurface(new_sample_rotated)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

h=gca;

h.Children(2)

ans =

Patch with properties: FaceColor: 'flat' FaceAlpha: 1 EdgeColor: 'none' LineStyle: '-' Faces: [5148×3 double] Vertices: [2576×3 double] Show all properties

rotate(h.Children(2),[1 0 0],45)

figure

isosurface(new_sample_rotated)

hold on

isosurface(new_sample_rotated)

axis equal

xlim([0 100])

ylim([0 100])

zlim([0 100])

h=gca;

rotate(h.Children(1),[1 0 0],35)

Carson Purnell 2022-6-13

I've found no way to convert this transformation into the real axis of the object, even matlab's method in the aerospace toolbox does not generate anything close to the real axis.

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