Angle between two 3D vectors

Question

Maciej Kupras 2022-10-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1839323-angle-between-two-3d-vectors

评论： Maciej Kupras 2022-10-30

I do have one column vector:

st_direction =
6320
7308
2579

And the matrix of (let's say) 5 vectors:

A =
-0.8903   -0.6071   -0.7037    0.4638    0.7759
0.3896    0.5431   -0.1126   -0.2208   -0.4987
0.2358   -0.5801    0.7015   -0.8580    0.3863

I need to calculate angles between vector st_direction and each column vector from A matrix, for example:

- angle between vector [0.6320 0.7308 0.2579] and vector [-0.8903, 0.3896, 0.2358].

Currently I'm trying to calculate it like that:

acos((dot(A(:,i),st_direction))/(norm(A(:,i))*norm(st_direction)))

But I think that something is wrong, because in later stages of a code I must check whether this angle is less than given variable:

acos((dot(A(:,i),st_direction))/(norm(A(:,i))*norm(st_direction)))<=deg2rad(fov_st)

I think that something is wrong because the program spits many point that when plotted on a graph are very far away. Is there any mistake?

Below there is an example for a greater amount of column vectors in matrix A (1000, generated as units vectors ) so it's easier to see. Red points are the points that satisfy the equation and the cyan line is the st_direction vector. As you can see, those points seem to be very randomly distributed.

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Answer 1

David Hill 2022-10-30

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https://ww2.mathworks.cn/matlabcentral/answers/1839323-angle-between-two-3d-vectors#answer_1087298

在 MATLAB Online 中打开

I don't see anything wrong. I assume you are using a loop.

st_direction =[0.6320;0.7308;0.2579];
 A =[-0.8903   -0.6071   -0.7037    0.4638    0.7759
0.3896    0.5431   -0.1126   -0.2208   -0.4987
0.2358   -0.5801    0.7015   -0.8580    0.3863];
for k=1:5
   Angles(k)=acos((dot(A(:,k),st_direction))/(norm(A(:,k))*norm(st_direction)));
end
Angles
Angles = 1×5
    1.7897    1.7076    1.9242    1.6604    1.3433

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Maciej Kupras 2022-10-30

Thank you very much for checking my code. As it turned out in a later loop I mistakenly assigned variables from different loops so wrong colums were placed in a new matrix. So stupid mistake but so common :P

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Answer 2

KALYAN ACHARJYA 2022-10-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1839323-angle-between-two-3d-vectors#answer_1087288

编辑：KALYAN ACHARJYA 2022-10-30

在 MATLAB Online 中打开

"I need to calculate angles between vector st_direction and each column vector from A matrix, for example:"

st_direction =[0.6320 0.7308 0.2579];
A =[-0.8903   -0.6071   -0.7037    0.4638    0.7759
    0.3896    0.5431   -0.1126   -0.2208   -0.4987
    0.2358   -0.5801    0.7015   -0.8580    0.3863];
angle_data=zeros(1,size(A,2)); % Memory Pre-Allocation
for i=1:size(A,2)
    angle_data(i)=atan2(norm(cross(st_direction,A(:,i))),dot(st_direction,A(:,i))); %radians
end
angle_data
angle_data = 1×5
    1.7897    1.7076    1.9242    1.6604    1.3433

Angle in Degrees ()

angle_data =
102.5408   97.8392  110.2498   95.1358   76.9647

Use atan2d instead of atan2

%If any issue let me know, be specific please!

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Maciej Kupras 2022-10-30

Thank you very much for checking my code. As it turned out in a later loop I mistakenly assigned variables from different loops so wrong colums were placed in a new matrix. So stupid mistake but so common :P

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