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Is there an “idiomatic†way to make x-y movement (e.g. arrow keys) correspond to rotations in $mathbbR^3$?
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Is there an "idiomatic" way to make x-y movement (e.g. arrow keys) correspond to rotations in $mathbbR^3$?
Intuitively the up, down, left and right of arrow keys would mean moving a $mathbbR^3$ vertex to the corresponding directions. However, since $mathbbR^3$ doesn't have clear "horizontal" and "vertical", but it also has depth, then I've been wondering how to "map" horizontal and vertical to $mathbbR^3$?
Or is this impossible?
linear-algebra
asked Aug 2 at 22:13
mavavilj
2,404729
add a comment |Â
up vote
1
down vote
favorite
Is there an "idiomatic" way to make x-y movement (e.g. arrow keys) correspond to rotations in $mathbbR^3$?
Intuitively the up, down, left and right of arrow keys would mean moving a $mathbbR^3$ vertex to the corresponding directions. However, since $mathbbR^3$ doesn't have clear "horizontal" and "vertical", but it also has depth, then I've been wondering how to "map" horizontal and vertical to $mathbbR^3$?
Or is this impossible?
linear-algebra
asked Aug 2 at 22:13
mavavilj
2,404729
If you want to rotate an object that the viewer is looking at, the up arrow usually means "rotate the axis pointing towards the viewer upwards". For example if the x-axis points right, the y-axis points up, and the z-axis points towards the viewer, then pressing the up arrow should cause a rotation about the negative x-axis.
– Rahul
Aug 2 at 22:20
Anyway this looks like it belongs on computergraphics.stackexchange.com.
– Rahul
Aug 2 at 22:21
There are threedegrees of freedom for rotations. Read the Euler angles Wikipedia article for details. I think that you will need three pairs of keys to indicate rotations.
– Somos
Aug 2 at 23:13
There are three degrees of freedom, but one of those can be realized by how long the user holds down the buttons.
– MJD
Aug 2 at 23:31
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Is there an "idiomatic" way to make x-y movement (e.g. arrow keys) correspond to rotations in $mathbbR^3$?
Intuitively the up, down, left and right of arrow keys would mean moving a $mathbbR^3$ vertex to the corresponding directions. However, since $mathbbR^3$ doesn't have clear "horizontal" and "vertical", but it also has depth, then I've been wondering how to "map" horizontal and vertical to $mathbbR^3$?
Or is this impossible?
linear-algebra
asked Aug 2 at 22:13
mavavilj
2,404729
Is there an "idiomatic" way to make x-y movement (e.g. arrow keys) correspond to rotations in $mathbbR^3$?
Intuitively the up, down, left and right of arrow keys would mean moving a $mathbbR^3$ vertex to the corresponding directions. However, since $mathbbR^3$ doesn't have clear "horizontal" and "vertical", but it also has depth, then I've been wondering how to "map" horizontal and vertical to $mathbbR^3$?
Or is this impossible?
linear-algebra
asked Aug 2 at 22:13
mavavilj
2,404729
asked Aug 2 at 22:13
mavavilj
2,404729
asked Aug 2 at 22:13
mavavilj
2,404729
asked Aug 2 at 22:13
mavavilj
2,404729
2,404729
If you want to rotate an object that the viewer is looking at, the up arrow usually means "rotate the axis pointing towards the viewer upwards". For example if the x-axis points right, the y-axis points up, and the z-axis points towards the viewer, then pressing the up arrow should cause a rotation about the negative x-axis.
– Rahul
Aug 2 at 22:20
Anyway this looks like it belongs on computergraphics.stackexchange.com.
– Rahul
Aug 2 at 22:21
There are threedegrees of freedom for rotations. Read the Euler angles Wikipedia article for details. I think that you will need three pairs of keys to indicate rotations.
– Somos
Aug 2 at 23:13
There are three degrees of freedom, but one of those can be realized by how long the user holds down the buttons.
– MJD
Aug 2 at 23:31
add a comment |Â
If you want to rotate an object that the viewer is looking at, the up arrow usually means "rotate the axis pointing towards the viewer upwards". For example if the x-axis points right, the y-axis points up, and the z-axis points towards the viewer, then pressing the up arrow should cause a rotation about the negative x-axis.
– Rahul
Aug 2 at 22:20
Anyway this looks like it belongs on computergraphics.stackexchange.com.
– Rahul
Aug 2 at 22:21
There are threedegrees of freedom for rotations. Read the Euler angles Wikipedia article for details. I think that you will need three pairs of keys to indicate rotations.
– Somos
Aug 2 at 23:13
There are three degrees of freedom, but one of those can be realized by how long the user holds down the buttons.
– MJD
Aug 2 at 23:31
If you want to rotate an object that the viewer is looking at, the up arrow usually means "rotate the axis pointing towards the viewer upwards". For example if the x-axis points right, the y-axis points up, and the z-axis points towards the viewer, then pressing the up arrow should cause a rotation about the negative x-axis.
– Rahul
Aug 2 at 22:20
If you want to rotate an object that the viewer is looking at, the up arrow usually means "rotate the axis pointing towards the viewer upwards". For example if the x-axis points right, the y-axis points up, and the z-axis points towards the viewer, then pressing the up arrow should cause a rotation about the negative x-axis.
– Rahul
Aug 2 at 22:20
Anyway this looks like it belongs on computergraphics.stackexchange.com.
– Rahul
Aug 2 at 22:21
Anyway this looks like it belongs on computergraphics.stackexchange.com.
– Rahul
Aug 2 at 22:21
There are threedegrees of freedom for rotations. Read the Euler angles Wikipedia article for details. I think that you will need three pairs of keys to indicate rotations.
– Somos
Aug 2 at 23:13
There are threedegrees of freedom for rotations. Read the Euler angles Wikipedia article for details. I think that you will need three pairs of keys to indicate rotations.
– Somos
Aug 2 at 23:13
There are three degrees of freedom, but one of those can be realized by how long the user holds down the buttons.
– MJD
Aug 2 at 23:31
There are three degrees of freedom, but one of those can be realized by how long the user holds down the buttons.
– MJD
Aug 2 at 23:31
add a comment |Â
1 Answer
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For rotations about lines through the origin, you can use just the four arrow keys.
You can specify the axis of rotation using a unit direction vector
$$ vecV=langle a,b,crangle=leftlanglesin(x),cos(x)sin(y),sqrt1-(sin^2(x)+cos^2(x)sin^2(y))rightrangle$$
Use one arrow key, let's say '$rightarrow$' to specify the value of $xge0$.
Use a second arrow key '$leftarrow$'to specify the value of $yge0$.
This allows the value of $a$ to cycle between values of $-1$ and $1$, the values of $b$ to cycle between values of $-sqrt1-a^2$ and $sqrt1-a^2 $ to express any direction $langle a,b,sqrt1-(a^2+b^2)rangle$ in $mathbbR^3$.
Then you can use the up and down arrows to indicate the amount $theta$ of positive or negative rotation about the axis.
To rotate about a line not passing through the origin one would first have to translate it to the origin, rotate, then do the inverse translation.
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
For rotations about lines through the origin, you can use just the four arrow keys.
You can specify the axis of rotation using a unit direction vector
$$ vecV=langle a,b,crangle=leftlanglesin(x),cos(x)sin(y),sqrt1-(sin^2(x)+cos^2(x)sin^2(y))rightrangle$$
Use one arrow key, let's say '$rightarrow$' to specify the value of $xge0$.
Use a second arrow key '$leftarrow$'to specify the value of $yge0$.
This allows the value of $a$ to cycle between values of $-1$ and $1$, the values of $b$ to cycle between values of $-sqrt1-a^2$ and $sqrt1-a^2 $ to express any direction $langle a,b,sqrt1-(a^2+b^2)rangle$ in $mathbbR^3$.
Then you can use the up and down arrows to indicate the amount $theta$ of positive or negative rotation about the axis.
To rotate about a line not passing through the origin one would first have to translate it to the origin, rotate, then do the inverse translation.
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
add a comment |Â
up vote
1
down vote
For rotations about lines through the origin, you can use just the four arrow keys.
You can specify the axis of rotation using a unit direction vector
$$ vecV=langle a,b,crangle=leftlanglesin(x),cos(x)sin(y),sqrt1-(sin^2(x)+cos^2(x)sin^2(y))rightrangle$$
Use one arrow key, let's say '$rightarrow$' to specify the value of $xge0$.
Use a second arrow key '$leftarrow$'to specify the value of $yge0$.
This allows the value of $a$ to cycle between values of $-1$ and $1$, the values of $b$ to cycle between values of $-sqrt1-a^2$ and $sqrt1-a^2 $ to express any direction $langle a,b,sqrt1-(a^2+b^2)rangle$ in $mathbbR^3$.
Then you can use the up and down arrows to indicate the amount $theta$ of positive or negative rotation about the axis.
To rotate about a line not passing through the origin one would first have to translate it to the origin, rotate, then do the inverse translation.
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
add a comment |Â
up vote
1
down vote
up vote
1
down vote
For rotations about lines through the origin, you can use just the four arrow keys.
You can specify the axis of rotation using a unit direction vector
$$ vecV=langle a,b,crangle=leftlanglesin(x),cos(x)sin(y),sqrt1-(sin^2(x)+cos^2(x)sin^2(y))rightrangle$$
Use one arrow key, let's say '$rightarrow$' to specify the value of $xge0$.
Use a second arrow key '$leftarrow$'to specify the value of $yge0$.
This allows the value of $a$ to cycle between values of $-1$ and $1$, the values of $b$ to cycle between values of $-sqrt1-a^2$ and $sqrt1-a^2 $ to express any direction $langle a,b,sqrt1-(a^2+b^2)rangle$ in $mathbbR^3$.
Then you can use the up and down arrows to indicate the amount $theta$ of positive or negative rotation about the axis.
To rotate about a line not passing through the origin one would first have to translate it to the origin, rotate, then do the inverse translation.
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
For rotations about lines through the origin, you can use just the four arrow keys.
You can specify the axis of rotation using a unit direction vector
$$ vecV=langle a,b,crangle=leftlanglesin(x),cos(x)sin(y),sqrt1-(sin^2(x)+cos^2(x)sin^2(y))rightrangle$$
Use one arrow key, let's say '$rightarrow$' to specify the value of $xge0$.
Use a second arrow key '$leftarrow$'to specify the value of $yge0$.
This allows the value of $a$ to cycle between values of $-1$ and $1$, the values of $b$ to cycle between values of $-sqrt1-a^2$ and $sqrt1-a^2 $ to express any direction $langle a,b,sqrt1-(a^2+b^2)rangle$ in $mathbbR^3$.
Then you can use the up and down arrows to indicate the amount $theta$ of positive or negative rotation about the axis.
To rotate about a line not passing through the origin one would first have to translate it to the origin, rotate, then do the inverse translation.
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
edited Aug 3 at 0:00
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
answered Aug 2 at 23:41
John Wayland Bales
12.8k21135
12.8k21135
add a comment |Â
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If you want to rotate an object that the viewer is looking at, the up arrow usually means "rotate the axis pointing towards the viewer upwards". For example if the x-axis points right, the y-axis points up, and the z-axis points towards the viewer, then pressing the up arrow should cause a rotation about the negative x-axis.
– Rahul
Aug 2 at 22:20
Anyway this looks like it belongs on computergraphics.stackexchange.com.
– Rahul
Aug 2 at 22:21
There are threedegrees of freedom for rotations. Read the Euler angles Wikipedia article for details. I think that you will need three pairs of keys to indicate rotations.
– Somos
Aug 2 at 23:13
There are three degrees of freedom, but one of those can be realized by how long the user holds down the buttons.
– MJD
Aug 2 at 23:31