Point cloud sequential transformation

Hi everyone,

I'm trying to apply two transformations to a point cloud, a translation A and then a rotation B. My issue is that the transformation matrix I get when using pcregistericp seems to be the opposite of what I expected (I get A*B instead of B*A). I'm not sure what the issue is, or if I'm misunderstanding the order of transformations in linear algebra.

xyzPoints=[];
for x=0:0.1:1
    for y=0:0.2:2
        z=x^2+y^3;
        xyzPoints=[xyzPoints;x y z];
    end    
end
ptCloud100 = pointCloud(xyzPoints);

%translation
A = [1 0 0 0; ...
     0 1 0 0; ...
     0 0 1 0; ...
     2 4 5 1];
tform = affine3d(A);
ptCloudOuttrans = pctransform(ptCloud100,tform);
%rotation
theta=deg2rad(70);
B = [cos(theta) 0 sin(theta) 0; ...
     0 1 0 0; ...
     -sin(theta) 0 cos(theta) 0; ...
     0 0 0 1];
tform = affine3d(B);
ptCloudOutrot = pctransform(ptCloudOuttrans,tform);
%ICP
[tform_inv,movingReg] = pcregistericp(ptCloudOutrot,ptCloud100,'Extrapolate',true,'MaxIterations',50);
t=invert(tform_inv);
disp(t.T);
%What I expected it to match
disp(B*A);
%what it matches
disp(A*B);

Answer 1

[Sulaymon Eshkabilov]

The answer is simple. MATLAB's accuracy is not absolute and thus, you have gotten difference. You can test this exercise:

theta=deg2rad(90);
...
    B*A
A*B
...

Good luck.

[Daniela Moreno]

Thank you for your response, but I'm not sure I understand your answer.

The reason why I'm confused it's because t.T (specially in the last row) seems to correspond much closer to A*B than to B*A which is what I would have expected because of B being applied after A.

I then changed the order of the transformations and got the opposite, so I'm not sure if I'm misunderstanding something about linear algebra or the transformation functions.