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Calculate the 3D angle between two vectors

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Paul Huter
Paul Huter 2017-3-5
编辑： Bruno Luong 2020-7-31
How do you calculate the angles between two vectors in order to generate a direction cosine matrix? I have MATLAB, Simulink, and Aerospace Toolkit/Toolbox. For reference, I am trying to use MATLAB to calculate a rotation matrix between the body frame of an object and (preferably) a fixed-frame or (not so preferably) an inertial-frame.

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回答（3 个）

Roger Stafford
Roger Stafford 2017-3-5
编辑：Roger Stafford 2017-3-5
The angle between two three-element vectors, P1 and P2, can be calculated using matlab in the following way:
a = atan2(norm(cross(P1,P2)),dot(P1,P2)); % Angle in radians
The angle will lie between 0 and pi radians. To get degrees use ‘atan2d’.
Note: However, the cosine of such an angle can be calculated as:
cosine of the angle = dot(P1,P2)/(norm(P1)*norm(P2))
No need to compute the angle itself.
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Zhafirah Ariana
Zhafirah Ariana 2020-7-31
I tried this and it worked! But when i use this for array it didn't work. Do you have any idea why this happened?
Bruno Luong
Bruno Luong 2020-7-31
编辑：Bruno Luong 2020-7-31
For array of size 3 x N where 3 rows are x-y-z coordinates you might replace the
  • CROSS with CROSS_DIM1
  • DOT with DOT_DIM1
  • NORM(X) with vecnorm(x, 2, 1) or sqrt(sum(x.^2,1)).
  • "^" with ".^"
CROSS_DIM1
function c = cross_dim1(a,b)
% c = cross_dim1(a,b)
% Calculate cross product along the first dimension
% NOTE: auto expansion allowed
c = zeros(max(size(a),size(b)));
c(1,:) = a(2,:).*b(3,:)-a(3,:).*b(2,:);
c(2,:) = a(3,:).*b(1,:)-a(1,:).*b(3,:);
c(3,:) = a(1,:).*b(2,:)-a(2,:).*b(1,:);
end % cross_dim1
and DOT_DIM1
function d = dot_dim1(a,b)
% d = dot_dim1(a,b)
% Calculate dot product along the first dimension
% NOTE: auto expansion allowed
d = sum(a.*b,1);
end % dot_dim1

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Image Analyst
Image Analyst 2017-3-5
Bingo
Bingo 2020-5-25
function r = vrrotvec(a, b, options)
%VRROTVEC Calculate a rotation between two vectors.
% R = VRROTVEC(A, B) calculates a rotation needed to transform
% a 3d vector A to a 3d vector B.
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John D'Errico
John D'Errico 2020-5-25
Not really. It is only there IF you just happen to have the correct toolbox.
help vrrotvec
'vrrotvec' requires Simulink 3D Animation.
Otherwise, you need to use the alteriatives.
Image Analyst
Image Analyst 2020-5-25
编辑：Image Analyst 2020-5-25
I don't have that toolbox. Simulink 3D Animation is not on the Products list on the right. I will add it.

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