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opencvimage-processingcomputer-vision
TimBluesWin
TimBluesWin

Reputation: 33

How can we find theta from rotation matrix?

According to OpenCV's documentation, solvePnp will return the rotation vector of the object pose from 3D-2D point correspondes. To obtain the rotation matrix, we can use Rodrigues method to convert the rotation vector to rotation matrix. According to OpenCV documentation, we can find theta using the following:

theta = norm(r)

But I thought norm(r) will find the magnitude of the vector r? If that's the case how can we find the angle from the magnitude of the vector r? Correct me if I am wrong. Thank you.

Upvotes: 0

Views: 683

Answers (1)

Francesco Callari
Francesco Callari

Reputation: 11785

Given a rotation vector r, its length (in Python, numpy.linalg.norm(r)) is the angle of rotation around the axis whose direction is the vector's one. The sense of the rotation obeys the "right hand rule": if your right hand makes a thumbs-up sign, with the thumb pointing as the vector, the other fingers wrap the vectors as the rotation (equivalently, it's the sense of rotation that makes an ordinary screw advance when its tip points as the vector).

The same rotation can be expressed as a 3x3 matrix, or as a triple of (Euler) angles or rotation about up to 3 orthogonal axes. There are ordinarily many different triples of Euler angles that represent the same rotation. Consult a textbook, or Wikipedia, for details.

Upvotes: 1

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