rotate vector around another vector The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)I want to rotate a point on a sphere surfaceGeometric interpretation of element by element division of one vector by anotherFind the line that passes by $P=(1,-2,3)$ and has angle $45$ and $60$ respectively with the $x$ and $y$ axisAn orthogonal transformation with determinant 1 rotate $mathbbR^3$ around an axis.Surface Area of unit n-sphere covered by rotating a unit vector around a fixed unit vector such that angle between the two vectors is always fixed.How to rotate in quaternions but for 2d version for arbitrary angle?Rotating direction vector in $mathbbR^n$Rotate a vector in 4D spaceVector operation question - rotate a 2d vector based on angleHow do I calculate a real angle between two Euler angles?
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rotate vector around another vector
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)I want to rotate a point on a sphere surfaceGeometric interpretation of element by element division of one vector by anotherFind the line that passes by $P=(1,-2,3)$ and has angle $45$ and $60$ respectively with the $x$ and $y$ axisAn orthogonal transformation with determinant 1 rotate $mathbbR^3$ around an axis.Surface Area of unit n-sphere covered by rotating a unit vector around a fixed unit vector such that angle between the two vectors is always fixed.How to rotate in quaternions but for 2d version for arbitrary angle?Rotating direction vector in $mathbbR^n$Rotate a vector in 4D spaceVector operation question - rotate a 2d vector based on angleHow do I calculate a real angle between two Euler angles?
$begingroup$
If I have vectors $a = (1,0,0)$, $b = (0,1,0)$, and $c=(0,0,1)$ and I want to rotate them counterclockwise at rate $r$ rad/sec around vector (1,1,1). What are the formulas for $a, b, c$?
euclidean-geometry
edited Sep 23 '11 at 21:08
NKS
3,7051626
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
$endgroup$
|
show 1 more comment
$begingroup$
If I have vectors $a = (1,0,0)$, $b = (0,1,0)$, and $c=(0,0,1)$ and I want to rotate them counterclockwise at rate $r$ rad/sec around vector (1,1,1). What are the formulas for $a, b, c$?
euclidean-geometry
edited Sep 23 '11 at 21:08
NKS
3,7051626
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
$endgroup$
$begingroup$
en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– user12205
Sep 23 '11 at 20:54
$begingroup$
^lol both of their links are broken: http://en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– anon
Sep 23 '11 at 21:58
$begingroup$
@anon Oops, I think I pasted the broken link by mistake :)
$endgroup$
– Srivatsan
Sep 23 '11 at 22:10
$begingroup$
weird, I just copy pasted it
$endgroup$
– user12205
Sep 23 '11 at 22:28
1
$begingroup$
@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full explanation: Rotation About an Arbitrary Axis in 3 Dimensions, inside.mines.edu/~gmurray/ArbitraryAxisRotation
$endgroup$
– user12205
Sep 23 '11 at 23:12
|
show 1 more comment
$begingroup$
If I have vectors $a = (1,0,0)$, $b = (0,1,0)$, and $c=(0,0,1)$ and I want to rotate them counterclockwise at rate $r$ rad/sec around vector (1,1,1). What are the formulas for $a, b, c$?
euclidean-geometry
edited Sep 23 '11 at 21:08
NKS
3,7051626
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
$endgroup$
If I have vectors $a = (1,0,0)$, $b = (0,1,0)$, and $c=(0,0,1)$ and I want to rotate them counterclockwise at rate $r$ rad/sec around vector (1,1,1). What are the formulas for $a, b, c$?
euclidean-geometry
euclidean-geometry
edited Sep 23 '11 at 21:08
NKS
3,7051626
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
edited Sep 23 '11 at 21:08
NKS
3,7051626
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
edited Sep 23 '11 at 21:08
NKS
3,7051626
edited Sep 23 '11 at 21:08
NKS
3,7051626
edited Sep 23 '11 at 21:08
NKS
3,7051626
3,7051626
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
asked Sep 23 '11 at 20:48
SuperGuySuperGuy
111
111
$begingroup$
en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– user12205
Sep 23 '11 at 20:54
$begingroup$
^lol both of their links are broken: http://en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– anon
Sep 23 '11 at 21:58
$begingroup$
@anon Oops, I think I pasted the broken link by mistake :)
$endgroup$
– Srivatsan
Sep 23 '11 at 22:10
$begingroup$
weird, I just copy pasted it
$endgroup$
– user12205
Sep 23 '11 at 22:28
1
$begingroup$
@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full explanation: Rotation About an Arbitrary Axis in 3 Dimensions, inside.mines.edu/~gmurray/ArbitraryAxisRotation
$endgroup$
– user12205
Sep 23 '11 at 23:12
|
show 1 more comment
$begingroup$
en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– user12205
Sep 23 '11 at 20:54
$begingroup$
^lol both of their links are broken: http://en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– anon
Sep 23 '11 at 21:58
$begingroup$
@anon Oops, I think I pasted the broken link by mistake :)
$endgroup$
– Srivatsan
Sep 23 '11 at 22:10
$begingroup$
weird, I just copy pasted it
$endgroup$
– user12205
Sep 23 '11 at 22:28
1
$begingroup$
@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full explanation: Rotation About an Arbitrary Axis in 3 Dimensions, inside.mines.edu/~gmurray/ArbitraryAxisRotation
$endgroup$
– user12205
Sep 23 '11 at 23:12
$begingroup$
en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– user12205
Sep 23 '11 at 20:54
$begingroup$
en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– user12205
Sep 23 '11 at 20:54
$begingroup$
^lol both of their links are broken: http://en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– anon
Sep 23 '11 at 21:58
$begingroup$
^lol both of their links are broken: http://en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– anon
Sep 23 '11 at 21:58
$begingroup$
@anon Oops, I think I pasted the broken link by mistake :)
$endgroup$
– Srivatsan
Sep 23 '11 at 22:10
$begingroup$
@anon Oops, I think I pasted the broken link by mistake :)
$endgroup$
– Srivatsan
Sep 23 '11 at 22:10
$begingroup$
weird, I just copy pasted it
$endgroup$
– user12205
Sep 23 '11 at 22:28
$begingroup$
weird, I just copy pasted it
$endgroup$
– user12205
Sep 23 '11 at 22:28
1
1
$begingroup$
@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full explanation: Rotation About an Arbitrary Axis in 3 Dimensions, inside.mines.edu/~gmurray/ArbitraryAxisRotation
$endgroup$
– user12205
Sep 23 '11 at 23:12
$begingroup$
@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full explanation: Rotation About an Arbitrary Axis in 3 Dimensions, inside.mines.edu/~gmurray/ArbitraryAxisRotation
$endgroup$
– user12205
Sep 23 '11 at 23:12
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
Wiki Rotation matrix has a lot of information on rotating around X, Y, Z separately by $alpha, beta, gamma$. These matrices can be multiplied together to get more complex rotations, but you will need to know how many rads to rotate around each axis.
And finally a rotation matrix that takes a vector and theta to create and can rotate a point/Vector around it. (I would like to know how this is Matrix is developed)
Rotation Matrix given Unit vector to rotate around and Theta
You will need to set up the rotation matrix $R$ and multiply $a' = Ra , b' = Rb , c' = Rc$. Use trial and error to figure +/- Theta to get clockwise rotation (This may depend on the "camera" orientation).
My own example on KA Shows a gray vector rotating around a red vector. Both are focused at the origin, so it creates a cone like shape.
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
$endgroup$
add a comment |
$begingroup$
As an alternative, you can use quaternions!
Quaternions are an extension of the complex numbers that very nicely represent rotations in three dimensions. If you want to rotate by an angle $theta$ around an axis $langle x, y, z rangle$, you first create a quaternion as follows:
$$q = cos(fractheta2) + x sin(fractheta2) i + y sin(fractheta2) j + z sin(fractheta2) k$$
Now you can apply this to a point $a$ to rotate it:
$$a' = q a barq$$
(where the overbar indicates the "conjugate": flip the signs on every term except the first).
Note: this is a very very short overview of the math behind this. If you're working in some sort of 3D modelling software like Unity, all of this math will be implemented for you, most likely in a quaternion library. Searching for "quaternion rotation" will get you more details.
answered Mar 8 at 3:17
DraconisDraconis
51528
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Wiki Rotation matrix has a lot of information on rotating around X, Y, Z separately by $alpha, beta, gamma$. These matrices can be multiplied together to get more complex rotations, but you will need to know how many rads to rotate around each axis.
And finally a rotation matrix that takes a vector and theta to create and can rotate a point/Vector around it. (I would like to know how this is Matrix is developed)
Rotation Matrix given Unit vector to rotate around and Theta
You will need to set up the rotation matrix $R$ and multiply $a' = Ra , b' = Rb , c' = Rc$. Use trial and error to figure +/- Theta to get clockwise rotation (This may depend on the "camera" orientation).
My own example on KA Shows a gray vector rotating around a red vector. Both are focused at the origin, so it creates a cone like shape.
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
$endgroup$
add a comment |
$begingroup$
Wiki Rotation matrix has a lot of information on rotating around X, Y, Z separately by $alpha, beta, gamma$. These matrices can be multiplied together to get more complex rotations, but you will need to know how many rads to rotate around each axis.
And finally a rotation matrix that takes a vector and theta to create and can rotate a point/Vector around it. (I would like to know how this is Matrix is developed)
Rotation Matrix given Unit vector to rotate around and Theta
You will need to set up the rotation matrix $R$ and multiply $a' = Ra , b' = Rb , c' = Rc$. Use trial and error to figure +/- Theta to get clockwise rotation (This may depend on the "camera" orientation).
My own example on KA Shows a gray vector rotating around a red vector. Both are focused at the origin, so it creates a cone like shape.
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
$endgroup$
add a comment |
$begingroup$
Wiki Rotation matrix has a lot of information on rotating around X, Y, Z separately by $alpha, beta, gamma$. These matrices can be multiplied together to get more complex rotations, but you will need to know how many rads to rotate around each axis.
And finally a rotation matrix that takes a vector and theta to create and can rotate a point/Vector around it. (I would like to know how this is Matrix is developed)
Rotation Matrix given Unit vector to rotate around and Theta
You will need to set up the rotation matrix $R$ and multiply $a' = Ra , b' = Rb , c' = Rc$. Use trial and error to figure +/- Theta to get clockwise rotation (This may depend on the "camera" orientation).
My own example on KA Shows a gray vector rotating around a red vector. Both are focused at the origin, so it creates a cone like shape.
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
$endgroup$
Wiki Rotation matrix has a lot of information on rotating around X, Y, Z separately by $alpha, beta, gamma$. These matrices can be multiplied together to get more complex rotations, but you will need to know how many rads to rotate around each axis.
And finally a rotation matrix that takes a vector and theta to create and can rotate a point/Vector around it. (I would like to know how this is Matrix is developed)
Rotation Matrix given Unit vector to rotate around and Theta
You will need to set up the rotation matrix $R$ and multiply $a' = Ra , b' = Rb , c' = Rc$. Use trial and error to figure +/- Theta to get clockwise rotation (This may depend on the "camera" orientation).
My own example on KA Shows a gray vector rotating around a red vector. Both are focused at the origin, so it creates a cone like shape.
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
answered Jun 28 '18 at 1:59
Cozy HarkinzCozy Harkinz
1
1
add a comment |
add a comment |
$begingroup$
As an alternative, you can use quaternions!
Quaternions are an extension of the complex numbers that very nicely represent rotations in three dimensions. If you want to rotate by an angle $theta$ around an axis $langle x, y, z rangle$, you first create a quaternion as follows:
$$q = cos(fractheta2) + x sin(fractheta2) i + y sin(fractheta2) j + z sin(fractheta2) k$$
Now you can apply this to a point $a$ to rotate it:
$$a' = q a barq$$
(where the overbar indicates the "conjugate": flip the signs on every term except the first).
Note: this is a very very short overview of the math behind this. If you're working in some sort of 3D modelling software like Unity, all of this math will be implemented for you, most likely in a quaternion library. Searching for "quaternion rotation" will get you more details.
answered Mar 8 at 3:17
DraconisDraconis
51528
$endgroup$
add a comment |
$begingroup$
As an alternative, you can use quaternions!
Quaternions are an extension of the complex numbers that very nicely represent rotations in three dimensions. If you want to rotate by an angle $theta$ around an axis $langle x, y, z rangle$, you first create a quaternion as follows:
$$q = cos(fractheta2) + x sin(fractheta2) i + y sin(fractheta2) j + z sin(fractheta2) k$$
Now you can apply this to a point $a$ to rotate it:
$$a' = q a barq$$
(where the overbar indicates the "conjugate": flip the signs on every term except the first).
Note: this is a very very short overview of the math behind this. If you're working in some sort of 3D modelling software like Unity, all of this math will be implemented for you, most likely in a quaternion library. Searching for "quaternion rotation" will get you more details.
answered Mar 8 at 3:17
DraconisDraconis
51528
$endgroup$
add a comment |
$begingroup$
As an alternative, you can use quaternions!
Quaternions are an extension of the complex numbers that very nicely represent rotations in three dimensions. If you want to rotate by an angle $theta$ around an axis $langle x, y, z rangle$, you first create a quaternion as follows:
$$q = cos(fractheta2) + x sin(fractheta2) i + y sin(fractheta2) j + z sin(fractheta2) k$$
Now you can apply this to a point $a$ to rotate it:
$$a' = q a barq$$
(where the overbar indicates the "conjugate": flip the signs on every term except the first).
Note: this is a very very short overview of the math behind this. If you're working in some sort of 3D modelling software like Unity, all of this math will be implemented for you, most likely in a quaternion library. Searching for "quaternion rotation" will get you more details.
answered Mar 8 at 3:17
DraconisDraconis
51528
$endgroup$
As an alternative, you can use quaternions!
Quaternions are an extension of the complex numbers that very nicely represent rotations in three dimensions. If you want to rotate by an angle $theta$ around an axis $langle x, y, z rangle$, you first create a quaternion as follows:
$$q = cos(fractheta2) + x sin(fractheta2) i + y sin(fractheta2) j + z sin(fractheta2) k$$
Now you can apply this to a point $a$ to rotate it:
$$a' = q a barq$$
(where the overbar indicates the "conjugate": flip the signs on every term except the first).
Note: this is a very very short overview of the math behind this. If you're working in some sort of 3D modelling software like Unity, all of this math will be implemented for you, most likely in a quaternion library. Searching for "quaternion rotation" will get you more details.
answered Mar 8 at 3:17
DraconisDraconis
51528
answered Mar 8 at 3:17
DraconisDraconis
51528
answered Mar 8 at 3:17
DraconisDraconis
51528
answered Mar 8 at 3:17
DraconisDraconis
51528
51528
add a comment |
add a comment |
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$begingroup$
en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– user12205
Sep 23 '11 at 20:54
$begingroup$
^lol both of their links are broken: http://en.wikipedia.org/wiki/Rotation_operator_(vector_space)
$endgroup$
– anon
Sep 23 '11 at 21:58
$begingroup$
@anon Oops, I think I pasted the broken link by mistake :)
$endgroup$
– Srivatsan
Sep 23 '11 at 22:10
$begingroup$
weird, I just copy pasted it
$endgroup$
– user12205
Sep 23 '11 at 22:28
1
$begingroup$
@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full explanation: Rotation About an Arbitrary Axis in 3 Dimensions, inside.mines.edu/~gmurray/ArbitraryAxisRotation
$endgroup$
– user12205
Sep 23 '11 at 23:12