Extract yaw/pitch/roll from faceAnchor in ARKit

Question

Using ARKit for facetracking, I get faceAnchor (ARFaceAnchor) as soon as the face is detected, which provides a simd_float4x4 matrix. I know about transformation matrices, and am also aware that the topic has been partially addressed (here: How to get values from simd_float4 in objective-c , and here: simd_float4x4 Columns), but is there a straighforward way to get yaw/pitch/rool values from the face anchor? (in order to feed my y/p/r values in the code below).

    func renderer(_ renderer: SCNSceneRenderer, didUpdate node: SCNNode, for anchor: ARAnchor) {
        let faceAnchor = anchor as? ARFaceAnchor
        let data = faceAnchor?.transform
        print(data!)
        let message = OSCMessage(
            OSCAddressPattern("/orientation"),
            yawValue,
            pitchValue,
            rollValue
        )
        client.send(message)
        print(message)
        
    }

FYI, OSCMessage comes from the SwiftOSC framework which is embedded in my project.

Answer 1

As there is apparently not (yet) a function provided by Apple for that purpose, it is a priori required to implement quaternion to euler angles computation. With these mathematical resources, and a radian-to-degrees conversion function, this can be implemented as an extension, as follows:

extension matrix_float4x4 {
    // Function to convert rad to deg
    func radiansToDegress(radians: Float32) -> Float32 {
        return radians * 180 / (Float32.pi)
    }
    var translation: SCNVector3 {
       get {
           return SCNVector3Make(columns.3.x, columns.3.y, columns.3.z)
       }
    }
    // Retrieve euler angles from a quaternion matrix
    var eulerAngles: SCNVector3 {
        get {
            // Get quaternions
            let qw = sqrt(1 + self.columns.0.x + self.columns.1.y + self.columns.2.z) / 2.0
            let qx = (self.columns.2.y - self.columns.1.z) / (qw * 4.0)
            let qy = (self.columns.0.z - self.columns.2.x) / (qw * 4.0)
            let qz = (self.columns.1.x - self.columns.0.y) / (qw * 4.0)

            // Deduce euler angles
            /// yaw (z-axis rotation)
            let siny = +2.0 * (qw * qz + qx * qy)
            let cosy = +1.0 - 2.0 * (qy * qy + qz * qz)
            let yaw = radiansToDegress(radians:atan2(siny, cosy))
            // pitch (y-axis rotation)
            let sinp = +2.0 * (qw * qy - qz * qx)
            var pitch: Float
            if abs(sinp) >= 1 {
                pitch = radiansToDegress(radians:copysign(Float.pi / 2, sinp))
            } else {
                pitch = radiansToDegress(radians:asin(sinp))
            }
            /// roll (x-axis rotation)
            let sinr = +2.0 * (qw * qx + qy * qz)
            let cosr = +1.0 - 2.0 * (qx * qx + qy * qy)
            let roll = radiansToDegress(radians:atan2(sinr, cosr))
            
            /// return array containing ypr values
            return SCNVector3(yaw, pitch, roll)
            }
    }
}