Calibration) How can i get to know multiplying order of Rotation matrix corresponding each axis?

First of all, English is not my mother tongue so i'm sorry about it.

I got Intrinsic, and Extrinsic Matrix using Matlab Calibration app. As a result, Extrinsic matrix is as follows.

My question is as follows.

1) I want to know the 'Order of multiplying of rotation for each axis' . To be Specific, Let's say Rotation about x-axis is R_x, about y-axis is R_y, about z-axis is R_z. Then as far as i know, The result of final Rotation Matrix is different according to order of multiply. That is, R = R_x * R_y * R_z is not same as R = R_z * R_y * R_x . But I need to know the order of multiply. Can anyone give me some insight about the order ?

2) And I have a question about the Unit. what is the Unit of Translation matrix? mm or cm? I guess it is cm, is it correct?

Also In Rotation matrix, the values like 0.0040 0.0345 .... are calculated as radian Unit or Degree Unit?

Thanks so much in Advance.

Answer 1

[Matt J]

(1) There is no single, unique ordering of Rx,Ry,Rz when you decompose a rotation matrix. You have 6 different choices for the ordering (actually 12 if you use more general Euler angles). Each choice gives a different result for Rx,Ry,Rz. The attached file can do the decomposition in whichever order you prefer.

(2) It would be in whatever units you used to measure the dimensions of the calibration pattern, e.g., the lengths of the checkerboard squares.

[은철 최]

Thank's for your answer. I understood with second question, but i still didn't know how to solve this problem.

What i want to do is to find a angel in 'radian' unit . As you see picture below, Using the final Rotation Matrix form, i want to find the angle alpha, beta, gamma in radian Unit. But how can i get to know the order?? Or which order should i choose???

Thanks.

[Matt J]

tb=rot2taitbryan(R,'ZYX')*pi/180;

alpha=tb(1);
beta=tb(2);
gamma=tb(3);