Why OpenCV uses Rodrigues rotation vector instead of Cayley's formula?

asked 2019-12-02 13:54:19 -0500

JamesBaxter gravatar image

I was a fan of Rodrigues rotation formula [1] until I learned about Cayley's formula for orthonormal matrices [2]. If I understand correctly Rodrigues is not meant necessarily to produce a 3x3 rotation matrix but to rotate a vector with a computationally light formula. So maybe OpenCV uses this formula internally to do all transformations? (skipping the calculation of the rotation matrix). Just

But when it comes to producing a 3x3 rotation matrix it seems, at a glance, that Cayley's formula is much simpler.

So why not use Cayley instead of Rodrigues?

[1] https://docs.opencv.org/ref/master/d9... [2] Murray, R. M.; Li, Z. & Sastry, S. S. A mathematical introduction to robotic manipulation Book, CRC press, 1994, 29, 214-222

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