Matrix multiplication between an operation matrix, such as the rotation matrix, and a coordinate list.

Hi

I would like to apply a 3D rotation operation, by matrix multiplication, on each of a element (rows) of coordinate list represented by a N x 3 vector.

For now I use a for-loop over all coordinates, see below, but I would prefer to do this in one operation.

BR

Thomas

y_rotation_matrix=@(theta) [cos(-theta) 0 sin(-theta);0 1 0;-sin(-theta) 0 cos(-theta)]; 

coordinate_list=rand(10,3)

hold on
xlabel('x')
ylabel('y')
zlabel('z')
plot3(coordinate_list(:,1),coordinate_list(:,2),coordinate_list(:,3));

rotated_coordinate_list=nan(size(coordinate_list));
theta0=.3
for q=1:size(coordinate_list,1)
    rotated_coordinate_list(q,:)=y_rotation_matrix(theta0)*coordinate_list(q,:)';    
end


plot3(rotated_coordinate_list(:,1),rotated_coordinate_list(:,2),rotated_coordinate_list(:,3));

Answer 1

[Paul]

y_rotation_matrix=@(theta) [cos(-theta) 0 sin(-theta);0 1 0;-sin(-theta) 0 cos(-theta)]; 
rng(100)
coordinate_list=rand(10,3);

rotated_coordinate_list=nan(size(coordinate_list));
theta0 = .3;
for q=1:size(coordinate_list,1)
    rotated_coordinate_list(q,:)=y_rotation_matrix(theta0)*coordinate_list(q,:)';    
end

Here is one option

r1 = (y_rotation_matrix(theta0)*coordinate_list.').';

Suprised that it's not exactly the same as result from the loop. Maybe some operations are done in a different order when multiplying two matrices like that?

r1 - rotated_coordinate_list

ans = 10×3

1.0e-15 * 0.0555 0 0 -0.0191 0 0 0 0 0 0 0 0 0 0 0 -0.0026 0 -0.0555 0 0 0 0 0 0 0 0 0.1110 0 0 0

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Here's another option.

r2 = coordinate_list*y_rotation_matrix(theta0).';

Also slightly different than original result

r2 - rotated_coordinate_list

ans = 10×3

1.0e-15 * 0.0555 0 0 -0.0191 0 0 0 0 0 0 0 0 0 0 0 -0.0026 0 -0.0555 0 0 0 0 0 0 0 0 0.1110 0 0 0

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But am slightly surprised that it's identical to the first method

r2 - r1

ans = 10×3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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[Matt J]

Suprised that it's not exactly the same as result from the loop. Maybe some operations are done in a different order when multiplying two matrices like that?

The way matrix operations are multithreaded depends on the size of the operands.