計算
回転の相互変換
オイラー角 → 回転行列 (EulerToMatrix)
- eulerAngle
- オイラー角 [roll, pitch, yaw]
- order
- 回転順 (0:XYZ, 1:XZY, 2:YXZ, 3:YZX, 4:ZXY, 5:ZYX)
- mat
- 回転行列
例
- eulerAngle
- [30, 30, 0]
- order
- 0
- mat
- \begin{bmatrix} 0.866& 0& 0.5 \\ 0.25& 0.866& -0.433 \\ -0.433& 0.5& 0.75 \end{bmatrix}
計算式
回転順 XYZ
\begin{align}
&R_{xyz}=R_xR_yR_z \\
&=
\begin{bmatrix}
cos\theta_y cos\theta_z & -cos\theta_y sin\theta_z & sin\theta_y \\
sin\theta_x sin\theta_y cos\theta_z+cos\theta_x sin\theta_z & -sin\theta_x sin\theta_y sin\theta_z+cos\theta_xcos\theta_z & -sin\theta_x cos\theta_y \\
-cos\theta_x sin\theta_y cos\theta_z+sin\theta_x sin\theta_z & cos\theta_x sin\theta_y sin\theta_z+sin\theta_x cos\theta_z & cos\theta_x cos\theta_y
\end{bmatrix}
\end{align}
回転順 XZY
\begin{align}
&R_{xzy}=R_xR_zR_y \\
&=
\begin{bmatrix}
cos\theta_y cos\theta_z & -sin\theta_z & sin\theta_y cos\theta_z \\
cos\theta_x cos\theta_y sin\theta_z+sin\theta_x sin\theta_y & cos\theta_x cos\theta_z & cos\theta_x sin\theta_y sin\theta_z-sin\theta_x cos\theta_y \\
sin\theta_x cos\theta_y sin\theta_z-cos\theta_x sin\theta_y & sin\theta_x cos\theta_z & sin\theta_x sin\theta_y sin\theta_z+cos\theta_x cos\theta_y
\end{bmatrix}
\end{align}
回転順 YXZ
\begin{align}
&R_{yxz}=R_yR_xR_z \\
&=
\begin{bmatrix}
sin\theta_x sin\theta_y sin\theta_z+cos\theta_y cos\theta_z & sin\theta_x sin\theta_y sin\theta_z-cos\theta_y sin\theta_z & cos\theta_x sin\theta_y \\
cos\theta_x sin\theta_z & cos\theta_x cos\theta_z & -sin\theta_z \\
sin\theta_x cos\theta_y sin\theta_z-sin\theta_y cos\theta_z & sin\theta_x cos\theta_y cos\theta_z+sin\theta_y sin\theta_z & cos\theta_x cos\theta_y
\end{bmatrix}
\end{align}
回転順 YZX
\begin{align}
&R_{yzx}=R_yR_zR_x \\
&=
\begin{bmatrix}
cos\theta_y cos\theta_z & -cos\theta_x cos\theta_y sin\theta_z+sin\theta_x sin\theta_y & sin\theta_x cos\theta_y sin\theta_z+cos\theta_x sin\theta_y \\
sin\theta_x & cos\theta_x cos\theta_z & -sin\theta_x cos\theta_z \\
-sin\theta_y cos\theta_z & cos\theta_x sin\theta_y sin\theta_z+sin\theta_x cos\theta_y & -sin\theta_x sin\theta_y sin\theta_z+cos\theta_x cos\theta_y
\end{bmatrix}
\end{align}
回転順 ZXY
\begin{align}
&R_{zxy}=R_zR_xR_y \\
&=
\begin{bmatrix}
-sin\theta_x sin\theta_y sin\theta_z+cos\theta_y cos\theta_z & -cos\theta_x sin\theta_z+ & sin\theta_x cos\theta_y sin\theta_z+sin\theta_y cos\theta_z \\
sin\theta_x sin\theta_y cos\theta_z+cos\theta_y sin\theta_z & cos\theta_x cos\theta_z & -sin\theta_x cos\theta_y cos\theta_z+sin\theta_y sin\theta_z \\
-cos\theta_x sin\theta_y & sin\theta_x & cos\theta_x cos\theta_y
\end{bmatrix}
\end{align}
回転順 ZYX
\begin{align}
&R_{zyx}=R_zR_yR_x \\
&=
\begin{bmatrix}
cos\theta_y cos\theta_z & sin\theta_x sin\theta_y cos\theta_z-cos\theta_x sin\theta_z & cos\theta_x sin\theta_y cos\theta_z+sin\theta_x sin\theta_z \\
cos\theta_y sin\theta_z & sin\theta_x sin\theta_y sin\theta_z+cos\theta_x cos\theta_z & cos\theta_x sin\theta_y sin\theta_z+sin\theta_x cos\theta_z \\
-sin\theta_y & sin\theta_x cos\theta_y & cos\theta_x cos\theta_y
\end{bmatrix}
\end{align}
回転行列 → オイラー角 (MatrixToEuler)
- mat
- 回転行列
- order
- 回転順 (0:XYZ, 1:XZY, 2:YXZ, 3:YZX, 4:ZXY, 5:ZYX)
- eulerAngle
- オイラー角 [roll, pitch, yaw]
例
- mat
- \begin{bmatrix} 0.866& 0& 0.5 \\ 0.25& 0.866& -0.433 \\ -0.433& 0.5& 0.75 \end{bmatrix}
- order
- 0
- eulerAngle
- [30, 30, 0]
計算式
回転行列の各要素は以下のように表します
\[
\begin{bmatrix}
m_{00}& m_{01}& m_{02} \\
m_{10}& m_{11}& m_{12} \\
m_{20}& m_{21}& m_{22} \\
\end{bmatrix}
\]
回転順 XYZ
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( -\frac{m_{12}}{m_{22}} \right) &(\cos \theta_y \neq 0) \\
\arctan \left( \frac{m_{21}}{m_{11}} \right) &(otherwise)
\end{cases} \\
\theta_y &= \arcsin (m_{02}) \\
\theta_z &= \begin{cases}
\arctan \left( -\frac{m_{01}}{m_{00}} \right) &(\cos \theta_y \neq 0) \\
0 &(otherwise)
\end{cases} \\
\end{align}
\]
回転順 XZY
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( \frac{m_{21}}{m_{11}} \right) &(\cos \theta_z \neq 0) \\
\arctan \left( -\frac{m_{12}}{m_{22}} \right) &(otherwise)
\end{cases} \\
\theta_y &= \begin{cases}
\arctan \left( \frac{m_{02}}{m_{00}} \right) &(\cos \theta_z \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_z &= \arcsin (-m_{01}) \\
\end{align}
\]
回転順 YXZ
\[\large
\begin{align}
\theta_x &= \arcsin (-m_{12}) \\
\theta_y &= \begin{cases}
\arctan \left( \frac{m_{02}}{m_{22}} \right) &(\cos \theta_x \neq 0) \\
\arctan \left( -\frac{m_{20}}{m_{00}} \right) &(otherwise)
\end{cases} \\
\theta_z &= \begin{cases}
\arctan \left( \frac{m_{10}}{m_{11}} \right) &(\cos \theta_x \neq 0) \\
0 &(otherwise)
\end{cases} \\
\end{align}
\]
回転順 YZX
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( -\frac{m_{12}}{m_{11}} \right) &(\cos \theta_z \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_y &= \begin{cases}
\arctan \left( -\frac{m_{20}}{m_{00}} \right) &(\cos \theta_z \neq 0) \\
\arctan \left( \frac{m_{02}}{m_{22}} \right) &(otherwise) \\
\end{cases} \\
\theta_z &= \arcsin (m_{10}) \\
\end{align}
\]
回転順 ZXY
\[\large
\begin{align}
\theta_x &= \arcsin (m_{21}) \\
\theta_y &= \begin{cases}
\arctan \left( -\frac{m_{20}}{m_{22}} \right) &(\cos \theta_x \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_z &= \begin{cases}
\arctan \left( -\frac{m_{01}}{m_{11}} \right) &(\cos \theta_x \neq 0) \\
\arctan \left( \frac{m_{10}}{m_{00}} \right) &(otherwise) \\
\end{cases} \\
\end{align}
\]
回転順 ZYX
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( \frac{m_{21}}{m_{22}} \right) &(\cos \theta_y \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_y &= \arcsin (-m_{20}) \\
\theta_z &= \begin{cases}
\arctan \left( \frac{m_{10}}{m_{00}} \right) &(\cos \theta_y \neq 0) \\
\arctan \left( -\frac{m_{01}}{m_{11}} \right) &(otherwise) \\
\end{cases} \\
\end{align}
\]
オイラー角 → クォータニオン (EulerToQuaternion)
- eulerAngle
- オイラー角 [roll, pitch, yaw]
- order
- 回転順 (0:XYZ, 1:XZY, 2:YXZ, 3:YZX, 4:ZXY, 5:ZYX)
- q
- クォータニオン [w, x, y, z]
例
- eulerAngle
- [30, 30, 0]
- order
- 0
- q
- q.w=0.933
q.x=0.25
q.y=0.25
q.z=0.067
計算式
クォータニオンは以下のように表します
\[
q =
\begin{bmatrix}
q_w \\
q_x \\
q_y \\
q_z \\
\end{bmatrix}
\]
回転順 XYZ
\[\large
\begin{bmatrix}
-\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
-\sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\end{bmatrix}
\]
回転順 XZY
\[\large
\begin{bmatrix}
\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
-\cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} - \sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\end{bmatrix}
\]
回転順 YXZ
\[\large
\begin{bmatrix}
\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
-\sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} - \sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\end{bmatrix}
\]
回転順 YZX
\[\large
\begin{bmatrix}
-\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
-\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\end{bmatrix}
\]
回転順 ZXY
\[\large
\begin{bmatrix}
-\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
-\cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} + \sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\end{bmatrix}
\]
回転順 ZYX
\[\large
\begin{bmatrix}
\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
\sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\cos \frac{\theta_z}{2} - \cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\sin \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} \\
-\sin \frac{\theta_x}{2}\sin \frac{\theta_y}{2}\cos \frac{\theta_z}{2} + \cos \frac{\theta_x}{2}\cos \frac{\theta_y}{2}\sin \frac{\theta_z}{2} \\
\end{bmatrix}
\]
クォータニオン → オイラー角 (QuaternionToEuler)
- q
- クォータニオン [w, x, y, z]
- order
- 回転順 (0:XYZ, 1:XZY, 2:YXZ, 3:YZX, 4:ZXY, 5:ZYX)
- eulerAngle
- オイラー角 [roll, pitch, yaw]
例
- q
- q.w=0.933
q.x=0.25
q.y=0.25
q.z=0.067 - order
- 0
- eulerAngle
- [30, 30, 0]
計算式
クォータニオンは以下のように表します
\[
q =
\begin{bmatrix}
q_w \\
q_x \\
q_y \\
q_z \\
\end{bmatrix}
\]
回転順 XYZ
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( -\frac{2q_yq_z-2q_xq_w}{2q_w^2+2q_z^2-1} \right) &(\cos \theta_y \neq 0) \\
\arctan \left( \frac{2q_yq_z+2q_xq_w}{2q_w^2+2q_y^2-1} \right) &(otherwise)
\end{cases} \\
\theta_y &= \arcsin (2q_xq_z+2q_yq_w) \\
\theta_z &= \begin{cases}
\arctan \left( -\frac{2q_xq_y-2q_zq_w}{2q_w^2+2q_x^2-1} \right) &(\cos \theta_y \neq 0) \\
0 &(otherwise)
\end{cases} \\
\end{align}
\]
回転順 XZY
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( \frac{2q_yq_z+2q_xq_w}{2q_w^2+2q_y^2-1} \right) &(\cos \theta_z \neq 0) \\
\arctan \left( -\frac{2q_yq_z-2q_xq_w}{2q_w^2+2q_z^2-1} \right) &(otherwise) \\
\end{cases} \\
\theta_y &= \begin{cases}
\arctan \left( \frac{2q_xq_z+2q_yq_w}{2q_w^2+2q_x^2-1} \right) &(\cos \theta_z \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_z &= \arcsin (-(2q_xq_y-2q_zq_w)) \\
\end{align}
\]
回転順 YXZ
\[\large
\begin{align}
\theta_x &= \arcsin (-(2q_yq_z-2q_xq_w)) \\
\theta_y &= \begin{cases}
\arctan \left( \frac{2q_xq_z+2q_yq_w}{2q_w^2+2q_z^2-1} \right) &(\cos \theta_x \neq 0) \\
\arctan \left( -\frac{2q_xq_z-2q_yq_w}{2q_w^2+2q_z^2-1} \right) &(otherwise) \\
\end{cases} \\
\theta_z &= \begin{cases}
\arctan \left( \frac{2q_xq_y+2q_zq_w}{2q_w^2+2q_y^2-1} \right) &(\cos \theta_x \neq 0) \\
0 &(otherwise)
\end{cases} \\
\end{align}
\]
回転順 YZX
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( -\frac{2q_yq_z-2q_xq_w}{2q_w^2+2q_y^2-1} \right) &(\cos \theta_z \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_y &= \begin{cases}
\arctan \left( -\frac{2q_xq_z-2q_yq_w}{2q_w^2+2q_x^2-1} \right) &(\cos \theta_z \neq 0) \\
\arctan \left( \frac{2q_xq_z+2q_yq_w}{2q_w^2+2q_z^2-1} \right) &(otherwise) \\
\end{cases} \\
\theta_z &= \arcsin (-(2q_xq_y+2q_zq_w)) \\
\end{align}
\]
回転順 ZXY
\[\large
\begin{align}
\theta_x &= \arcsin (2q_yq_+2q_xq_w) \\
\theta_y &= \begin{cases}
\arctan \left( -\frac{2q_xq_z-2q_yq_w}{2q_w^2+2q_z^2-1} \right) &(\cos \theta_x \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_z &= \begin{cases}
\arctan \left( -\frac{2q_xq_y-2q_zq_w}{2q_w^2+2q_y^2-1} \right) &(\cos \theta_x \neq 0) \\
\arctan \left( \frac{2q_xq_y+2q_zq_w}{2q_w^2+2q_x^2-1} \right) &(otherwise) \\
\end{cases} \\
\end{align}
\]
回転順 ZYX
\[\large
\begin{align}
\theta_x &= \begin{cases}
\arctan \left( \frac{2q_yq_z+2q_xq_w}{2q_w^2+2q_z^2-1} \right) &(\cos \theta_y \neq 0) \\
0 &(otherwise)
\end{cases} \\
\theta_y &= \arcsin (-(2q_xq_z-2q_yq_w)) \\
\theta_z &= \begin{cases}
\arctan \left( \frac{2q_xq_y+2q_zq_w}{2q_w^2+2q_x^2-1} \right) &(\cos \theta_y \neq 0) \\
\arctan \left( -\frac{2q_xq_y-2q_zq_w}{2q_w^2+2q_y^2-1} \right) &(otherwise) \\
\end{cases} \\
\end{align}
\]
クォータニオン → 回転行列 (QuaternionToMatrix)
- q
- クォータニオン [w, x, y, z]
- mat
- 回転行列
例
- q
- q.w=0.933
q.x=0.25
q.y=0.25
q.z=0.067
- mat
- \begin{bmatrix} 0.866& 0& 0.5 \\ 0.25& 0.866& -0.433 \\ -0.433& 0.5& 0.75 \end{bmatrix}
計算式
\[\large \begin{bmatrix} 2q_w^2+2q_x^2-1& 2q_xq_y-2q_zq_w& 2q_xq_z+2q_yq_w \\ 2q_xq_y+2q_zq_w& 2q_w^2+2q_y^2-1& 2q_yq_z-2q_xq_w \\ 2q_xq_z-2q_yq_w& 2q_yq_z+2q_xq_w& 2q_w^2+2q_z^2-1 \\ \end{bmatrix} \]
回転行列 → クォータニオン (MatrixToQuaternion)
- mat
- 回転行列
- conv
- 変換候補 (0-3)
- q
- クォータニオン [w, x, y, z]
例
- mat
- \begin{bmatrix} 0.866& 0& 0.5 \\ 0.25& 0.866& -0.433 \\ -0.433& 0.5& 0.75 \end{bmatrix}
- conv
- 0
- q
- q.w=0.933
q.x=0.25
q.y=0.25
q.z=0.067
計算式
conv=0 \[\Large q= \begin{bmatrix} \frac{m_{21}-m_{12}}{2\sqrt{m_{00}-m_{11}-m_{22}+1}} \\ \frac{\sqrt{m_{00}-m_{11}-m_{22}+1}}{2} \\ \frac{m_{10}-m_{01}}{2\sqrt{m_{00}-m_{11}-m_{22}+1}} \\ \frac{m_{02}-m_{20}}{2\sqrt{m_{00}-m_{11}-m_{22}+1}} \\ \end{bmatrix} \] conv=1 \[\Large q= \begin{bmatrix} \frac{m_{02}-m_{20}}{2\sqrt{-m_{00}+m_{11}-m_{22}+1}} \\ \frac{m_{10}-m_{01}}{2\sqrt{-m_{00}+m_{11}-m_{22}+1}} \\ \frac{\sqrt{-m_{00}+m_{11}-m_{22}+1}}{2} \\ \frac{m_{21}-m_{12}}{2\sqrt{-m_{00}+m_{11}-m_{22}+1}} \\ \end{bmatrix} \] conv=2 \[\Large q= \begin{bmatrix} \frac{m_{10}-m_{01}}{2\sqrt{-m_{00}-m_{11}+m_{22}+1}} \\ \frac{m_{02}-m_{20}}{2\sqrt{-m_{00}-m_{11}+m_{22}+1}} \\ \frac{m_{21}-m_{12}}{2\sqrt{-m_{00}-m_{11}+m_{22}+1}} \\ \frac{\sqrt{-m_{00}-m_{11}+m_{22}+1}}{2} \\ \end{bmatrix} \] conv=3 \[\Large q= \begin{bmatrix} \frac{\sqrt{m_{00}+m_{11}+m_{22}+1}}{2} \\ \frac{m_{21}-m_{12}}{2\sqrt{m_{00}+m_{11}+m_{22}+1}} \\ \frac{m_{02}-m_{20}}{2\sqrt{m_{00}+m_{11}+m_{22}+1}} \\ \frac{m_{10}-m_{01}}{2\sqrt{m_{00}+m_{11}+m_{22}+1}} \\ \end{bmatrix} \]
参考URL
Quita 回転行列、クォータニオン、オイラー角の相互変換 https://qiita.com/aa_debdeb/items/3d02e28fb9ebfa357eaf