how to convert a rotation matrix to a rotation vector

In matlab function rodriguesMatrixToVector. There are some confusion I had about the code.

1. in comment: " % r = theta * v / |v|, where (w, v) is a unit quaternion". Where is the variable "w" ?

2. what does this equation from and mean? I didn't get it.

Answer 1

[James Tursa]

I can't find the computeRotationVectorForAnglesCloseToPi( ) function. Where is this from?

1. The "(w,v) is a unit quaternion" statement is basically telling you that w is the scalar part of the quaternion and v is the vector part of the quaternion, so v / |v| is the rotation Eigen axis. I.e., the statement is generic in nature to tell you what v is in relation to a quaternion and there is no actual w in the code.
2. Without seeing the entire code, I cannot be sure what this is. What is t? How did r get calculated? If I were to hazard a guess, I might expect it to be a small angle limiting formula to handle the cases near 0.