回転行列からオイラー角を求める

// Z軸でz（ラジアン）回転させる行列
Rz = {cos(z),  sin(z), 0,
      -sin(z), cos(z), 0,
      0,       0,      1}

// X軸方向にx（ラジアン）回転させる行列
Rx = {1, 0,       0,
      0, cos(x),  sin(x),
      0, -sin(x), cos(x)}

RzRx = {cos(z),  sin(z)*cos(x), sin(z)*sin(x),
        -sin(z), cos(z)*cos(x), cos(z)*sin(x),
        0,       -sin(x),       cos(x)}

// Y軸方向にy（ラジアン）回転させる行列
Ry = {cos(y), 0, -sin(y),
      0,      1, 0,
      sin(y), 0, cos(y)}

RzRxRy = {cos(z)*cos(y)+sin(z)*sin(x)*sin(y),  sin(z)*cos(x), -cos(z)sin(y)+sin(z)*sin(x)*cos(y),
          -sin(z)*cos(y)+cos(z)*sin(x)*sin(y), cos(z)*cos(x), sin(z)*sin(y)+cos(z)*sin(x)*cos(y),
          cos(x)*sin(y),                       -sin(x),       cos(x)*cos(y)}

// @upと@Nの外積からx軸のベクトルをつくる
vector L = cross(@up, @N)
 
RzRxRy = {L.x,  L.y,  L.z,
          up.x, up.y, up.z,
          N.x,  N.y,  N.z}

L.x = cos(z)*cos(y)+sin(z)*sin(x)*sin(y)
L.y = sin(z)*cos(x)
L.z = -cos(z)sin(y)+sin(z)*sin(x)*cos(y)
 
up.x = -sin(z)*cos(y)+cos(z)*sin(x)*sin(y)
up.y = cos(z)*cos(x)
up.z = sin(z)*sin(y)+cos(z)*sin(x)*cos(y)
 
N.x = cos(x)*sin(y)
N.y = -sin(x)
N.z = cos(x)*cos(y)

// 行列を構成する３つの軸ベクトルをつくる
@N = normalize(set(1, 0, 1));
@up = normalize(set(-1, 1, 0));
@left = cross(@up, @N);
@up = cross(@N, @left); // 90度で交わるようにupベクトルを補正する
 
// オイラー角を計算する
v@rot.x = degrees(-asin(@N.y));
v@rot.y = degrees(atan2(@N.x, @N.z));
v@rot.z = degrees(atan2(v@left.y, @up.y));
 
printf('@rot:' + sprintf('%g', @rot) + '\n');
//@rot:{-0,45,35.2644}