Angle between two vectors in 3d

Hello,

I have two vectors in 3d and i want to find the angle between those two vectors.

Thanks in advance

Answer 1

[Jan]

Or:

angle = atan2(norm(cross(a,b)), dot(a,b))

See this compact discussion about this topic: CSSM: Angle between two vectors . Only 71 replies (Google finds 89 replies, so I assume 18 spam messages?) and 68300 views currently...

[EDITED]: W. Kahan suggested in his paper "Mindeless.pdf":

2 * atan(norm(x*norm(y) - norm(x)*y) / norm(x * norm(y) + norm(x) * y))

[developer]

Thanks simon :)

actually i have seen this thread before and confused with

angle = atan2(norm(cross(a,b)), dot(a,b))

and

acos(dot(v1, v2) / (norm(v1) * norm(v2)))

[Jan]

The ATAN2 approach has a higher numerical stability, but it is slower. Although Matlab states in the documentation, that ACOS from the FDLIBM library is use, I cannot reproduce the results exactly using the source from netlib.org. But the differences concern the angles very near to 0 and 180 degrees.

[TAEYUN]

hey simon I have some questions if i have 3values of x,y,z how can i find angle between two 3d vectors?

[Bineet_Mehra]

I have u1 v1 w1(velocity components) volumetric data. Size of u1 is NxNxN (N is 100) and same is true frol v1 and w1.

I have one more case of u2, v2, w2, each one of size NxNxN. both these data sets are obtained from TriScatteredInterp and meshgrid. Basically i plotted streamlines for these two cases and now i want to see how much deviation is there between these streamlines (from case 1 to 2.). I need to find the angle between them at the points given by meshgrid. But cross product wont work (A and B must have at least one dimension of length 3.).. any suggestion ?? Thanks a lot

[Jan]

@Bineet_Mehra: Please open a new thread for a new problem. Otherwise you cannot accept an answer as a solution.

I guess you want:

vel1 = [u1(:), v1(:), w1(:)]
vel2 = [u2(:), v2(:), w2(:)]

Now the cross-product should work.

[Bineet_Mehra]

@Jan Simon, Thanks for your suggestion. I shall open a new thread and will try the solution given by you.

Thanks

[Bineet_Mehra]

http://fr.mathworks.com/matlabcentral/answers/281635-cross-product-multi-dim-data new thread and new answer

[Dyuman Joshi]

@Jan the CSSM thread you linked does not exist anymore.

Do you happen to have an archived link for that thread?

I am unable to find the thread by simply searching the title, on the Google Groups (CSSM archive)

[Bruno Luong]

@Dyuman Joshi I guess this is the thread https://groups.google.com/g/comp.soft-sys.matlab/c/zNbUui3bjcA/m/c0HV_bHSx9cJ

Answer 2

[Lucas García]

You can use the subspace function to find the angle between two subspaces:

>> subspace([1;0;0],[0;1;0])

ans =

    1.5708

[Yadu Bhusal]

I have 3 points in a line( suppose) and one calculations point separately. A(1,1,1)B(2,2,2)C(3 3 3) in a line and P( 5 5 5) as separate. I want to calculate angle A which is subtended by distance AP. And similar for BP,CP. Is it possible to find angles or make program to calculate these angles at once?

Answer 3

[David Young]

acos(dot(v1, v2) / (norm(v1) * norm(v2)))

EDIT: Having seen Jan Simon's reply, and the long thread at CSSM that he refers to, I realise that the formula I proposed is not a particularly good one. The two methods in Jan's reply are both likely to be preferable.

[developer]

Thanks actually i have seen the post referred by Jan simon

and confused that what is the difference between

angle = atan2(norm(cross(a,b)), dot(a,b))

and

acos(dot(v1, v2) / (norm(v1) * norm(v2)))

[Jan]

Mathematically identical, but numerically more stable, when the vectors have very different lengths:

acos(dot(v1 / norm(v1), v2 / norm(v2)))

Answer 4

[rashi]

hi I want to find the angle in azimuth and elevation plane between wo vectors in 3d. please help