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How to calculate the rotation of a vector?
Given our unit vectors, we note that cosθ = A ⋅ B, and sinθ = | | A × B | |. Thus G = ( A ⋅ B − ‖A × B‖ 0 ‖A × B‖ A ⋅ B 0 0 0 1).
Is there a unique matrix to rotate a vector?
There is NO unique Matrix that could rotate one unit vector to another. Simply because the solution to 3 equations with 9 arguments does not unique. Since you have the plane (not only the normal vector), a way to find a unique rotation matrix between two coordinate system would be: do the non-unique rotation twice!
How to find a unique rotation matrix between two coordinate systems?
Since you have the plane (not only the normal vector), a way to find a unique rotation matrix between two coordinate system would be: do the non-unique rotation twice! Find a orthogonal vector in the same plane of interest with A and B respectively.
Which is the correct way to rotate an image clockwise?
Edit: There is a problem with the image! it was supposed to be rotated clockwise by right hand thumb rule unlike how it is shown in the image (but there shouldn’t be much of a difference in the solution). Right hand thumb rule: “Wrap the fingers of your right hand around vector b such that your thumb points in the direction of vector b.
Rotations are done via the standard 2D rotation equations: x’ = x cos (theta) – y sin (theta) y’ = y cos (theta) + x sin (theta) But for some reason, after the second rotation, the line (in yellow) doesn’t line up with the green line (the original target of rotating this vector).
Is it possible to rotate a 3D vector around an axis?
When checking the angle theta2, it comes out around 35 degrees which looks plausible. I am not quite clear on your question, but hopefully this should help. If you want to rotate a 3D vector around a particular axis, take advantage of matrix transformations instead of element wise (like you have written above).
When to apply 2D rotation to 2D vector?
It only really makes sense to apply a 2D rotation to a 2D vector to obtain the transformed coordinates. The result of a matrix product is defined only when the left hand matrix has column count equal to right hand matrix row count.
Which is the optimized function in scipy.optimize?
The scipy.optimize package provides several commonly used optimization algorithms. A detailed listing is available: scipy.optimize (can also be found by help (scipy.optimize) ). The minimize function provides a common interface to unconstrained and constrained minimization algorithms for multivariate scalar functions in scipy.optimize.