ARKit Calc euler angles from rotation matrix in YXZ world

问题

I need help in math in general for euler angles and specifically in ARKit.

I looked at many references for calculation of euler angles but I wondered why apple in its tutorial calculated yaw from atan2(r11, r12) as follow:

let yaw = atan2f(camera.transform.columns.0.x, camera.transform.columns.1.x)

If I need to calculate pitch or roll, for example how?

I need to understand yaw and why they not always depends on yaw = camera.eularAngle.y

Please check this code and questions in comments, I'm very confused !

  // why based on this?
            let tilt = abs(camera.eulerAngles.x)
             
            // why * 0.65 or  * 0.75
            let threshold1: Float = .pi / 2 * 0.65
            let threshold2: Float = .pi / 2 * 0.75
             
            // calculate yaw angle
            let yaw = atan2f(camera.transform.columns.0.x, camera.transform.columns.1.x)
          
         
            var angle: Float = 0
            
            switch tilt {
                case 0..<threshold1:
                    angle = camera.eulerAngles.y
                case threshold1..<threshold2:
                    let relativeInRange = abs((tilt - threshold1) / (threshold2 - threshold1))
                    let normalizedY = normalize(camera.eulerAngles.y, forMinimalRotationTo: yaw)
                    angle = normalizedY * (1 - relativeInRange) + yaw * relativeInRange
                default:
                    angle = yaw
            }
        
            self.rotation = SCNVector4(0, 1, 0, angle)

Does the order of rotations : rx ry rz OR ry rz rx could be the result of other equations for extracting euler angles from rotation matrix ?? and what's about mobile movements? We don't know what's the order of rotations? ( Note that, I have strong background in transfomation matrix and openGL)

I know atan2 what it means, I know that matrix of y rotation for r12 or column.1.x is should be zero:

| cos a  0   sin a |
| 0      1   0     |
| -sin a 1   cos a |  
         
          ||

   | r11 r12 r13 |
   | r21 r22 r23 |
   | r31 r32 r33 | 

In most references consider z-up so it's the yaw, but in arkit y-up, so what's the difference for calculation ??

I just need to understand,I don't need code to work !! if anyone helps me I will be really really apprciate him.

来源：https://stackoverflow.com/questions/63758384/arkit-calc-euler-angles-from-rotation-matrix-in-yxz-world