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!

Accepted Answer

James Tursa
James Tursa on 17 Nov 2021
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 Comments
Vignesh Radhakrishnan
Vignesh Radhakrishnan on 21 Apr 2023
Can I get the point y again from x using the inverse of the output of vrrotvec or vrrotvec2mat?
James Tursa
James Tursa on 12 May 2023
Edited: James Tursa on 12 May 2023
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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