[Graphics/Math] Euler to Quaternion, Quaternion to Euler

https://stackoverflow.com/questions/11103683/euler-angle-to-quaternion-then-quaternion-to-euler-angle

Euler angle to Quaternion then Quaternion to euler angle

http://marc-b-reynolds.github.io/math/2017/04/18/TaitEuler.html

Converting to Euler & Tait-Bryan

http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm

Maths - Conversion Quaternion to Euler - Martin Baker

 

Javascript로 옮기면 이렇다.

function threeAxisRotote(r11, r12, r21, r31, r32){
    return [
        Math.atan2(r11, r12),
        Math.asin(r21),
        Math.atan2(r31, r32),
    ];
}

function quaternionToEuler(q, order) {
    switch(order){
    case "ZYX":
        return threeAxisRotote(
            2*(q.x*q.y + q.w*q.z),
            q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
            -2*(q.x*q.z - q.w*q.y),
            2*(q.y*q.z + q.w*q.x),
            q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z
        );
    case "ZXY":
        return threeAxisRotote(
            -2*(q.x*q.y - q.w*q.z),
            q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
            2*(q.y*q.z + q.w*q.x),
            -2*(q.x*q.z - q.w*q.y),
            q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z
        );
    case "YXZ":
        return threeAxisRotote(
            2*(q.x*q.z + q.w*q.y),
            q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
            -2*(q.y*q.z - q.w*q.x),
            2*(q.x*q.y + q.w*q.z),
            q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z
        );
    case "YZX":
        return threeAxisRotote(
            -2*(q.x*q.z - q.w*q.y),
            q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
            2*(q.x*q.y + q.w*q.z),
            -2*(q.y*q.z - q.w*q.x),
            q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z
        );
    case "XYZ":
        return threeAxisRotote(
            -2*(q.y*q.z - q.w*q.x),
            q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
            2*(q.x*q.z + q.w*q.y),
            -2*(q.x*q.y - q.w*q.z),
            q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z
        );
    case "XZY":
        return threeAxisRotote(
            2*(q.y*q.z + q.w*q.x),
            q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
            -2*(q.x*q.y - q.w*q.z),
            2*(q.x*q.z + q.w*q.y),
            q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z
        );
    }
}

Euler --(XYZ)--> Quaternion --(ZYX)--> Euler 로 변환해야 같은 euler 값을 꺼낼 수 있다.

그리고 위 레퍼런스 코드가 xyz가 아니라 zyx 순으로 읽고 사용하는 것 같다.