ロドリゲスの回転公式
Last updated: 2026-08-14
あるベクトルを任意の単位ベクトルを軸に回転させるよ
1.
O
P
⃗
\vec{OP}
O
P
の
n
⃗
\vec{n}
n
への
正射影ベクトル
O
O
′
⃗
\vec{OO'}
O
O
′
を求める
2.
O
O
′
⃗
−
O
P
⃗
=
O
′
P
⃗
\vec{OO'} - \vec{OP} = \vec{O'P}
O
O
′
−
O
P
=
O
′
P
3.
n
⃗
×
O
′
P
⃗
=
O
′
Q
⃗
=
n
⃗
×
r
⃗
\vec{n} \times \vec{O'P} = \vec{O'Q} = \vec{n} \times \vec{r}
n
×
O
′
P
=
O
′
Q
=
n
×
r
4.
O
′
P
⃗
c
o
s
θ
+
O
′
Q
⃗
s
i
n
θ
=
O
′
P
′
⃗
\vec{O'P}cos{\theta} + \vec{O'Q}sin{\theta} = \vec{O'P'}
O
′
P
cos
θ
+
O
′
Q
s
in
θ
=
O
′
P
′
互いに直行同士
5.
O
O
′
⃗
+
O
′
P
′
⃗
=
O
P
′
⃗
=
(
r
⃗
⋅
n
⃗
)
n
⃗
+
(
r
−
(
r
⃗
⋅
n
⃗
)
n
⃗
)
c
o
s
θ
+
(
n
⃗
×
r
⃗
)
s
i
n
θ
\vec{OO'} + \vec{O'P'} = \vec{OP'} = (\vec{r} \cdot \vec{n})\vec{n} + (r-(\vec{r} \cdot \vec{n})\vec{n})cos\theta + (\vec{n} \times \vec{r})sin\theta
O
O
′
+
O
′
P
′
=
O
P
′
=
(
r
⋅
n
)
n
+
(
r
−
(
r
⋅
n
)
n
)
cos
θ
+
(
n
×
r
)
s
in
θ
さらに式が奇麗になるっぽいけどわからん
https://scrapbox.io/ cooking time
https://www.desmos.com/3d/u9szlnluua?lang=ja
ぽえ
🔗
https://soramamenatan.hatenablog.com/entry/2020/11/28/193256
ありがとねん