How does vrrotvec calculate rotation?

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Can anybody describe the math behind vrrotvec? The documentation for this function is very sparse and I would like to know how the rotational transformation is being calculated for my own confiendence in my code.
Thanks!

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James Tursa
James Tursa 2021-11-17
It is a simple algorithm that uses the cross product for the axis (normalized), and the dot product is used to calculate the angle. I.e., vrrotvec(x,y) is equivalent to the following (but with error checking etc.)
rotation axis = cross(x,y)/norm(cross(x,y))
rotation angle = acos(dot(x,y)/(norm(x)*norm(y)))
then these are concatenated into a 4-element vector
  3 个评论
Vignesh Radhakrishnan
Can I get the point y again from x using the inverse of the output of vrrotvec or vrrotvec2mat?
James Tursa
James Tursa 2023-5-12
编辑:James Tursa 2023-5-12
Do you mean like this?
x = rand(3,1); x = x/norm(x)
x = 3×1
0.7639 0.6442 0.0390
y = rand(3,1); y = y/norm(y)
y = 3×1
0.6172 0.5255 0.5856
r = vrrotvec(x,y)
r = 1×4
0.6445 -0.7646 0.0068 0.5866
m = vrrotvec2mat(r)
m = 3×3
0.9023 -0.0862 -0.4225 -0.0786 0.9306 -0.3576 0.4240 0.3559 0.8328
m * x
ans = 3×1
0.6172 0.5255 0.5856
norm(ans-y)
ans = 1.5701e-16

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