Using 6th dimensional vector to rotate a tesseract
$begingroup$
I'm trying to rotate a tesseract in 4D space for a project.
This shows I can use bivectors to "to generate rotations in four dimensions." Following exterior algebra and finding the wedge product, I've managed to get a 6D vector that supposedly describes my 4D rotation. This is great, except I have no idea how to use the 6D vector to rotate my 4D object.
I've looked at many links but none describe how to actually do the rotation using the wedge product. I'd like to stay away from matrix rotations.
- Rotating a 4 dimensional point?
- https://arxiv.org/pdf/1408.5799.pdf
- https://arxiv.org/pdf/1103.5263.pdf
- https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space
- https://en.wikipedia.org/wiki/Bivector#Four_dimensions
- http://eusebeia.dyndns.org/4d/vis/10-rot-1
How can I use the 6D vector to rotate the 4D object?
rotations exterior-algebra dimension-theory
asked Dec 9 '18 at 5:30
anonanon
6
$endgroup$
add a comment |
$begingroup$
I'm trying to rotate a tesseract in 4D space for a project.
This shows I can use bivectors to "to generate rotations in four dimensions." Following exterior algebra and finding the wedge product, I've managed to get a 6D vector that supposedly describes my 4D rotation. This is great, except I have no idea how to use the 6D vector to rotate my 4D object.
I've looked at many links but none describe how to actually do the rotation using the wedge product. I'd like to stay away from matrix rotations.
- Rotating a 4 dimensional point?
- https://arxiv.org/pdf/1408.5799.pdf
- https://arxiv.org/pdf/1103.5263.pdf
- https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space
- https://en.wikipedia.org/wiki/Bivector#Four_dimensions
- http://eusebeia.dyndns.org/4d/vis/10-rot-1
How can I use the 6D vector to rotate the 4D object?
rotations exterior-algebra dimension-theory
asked Dec 9 '18 at 5:30
anonanon
6
$endgroup$
$begingroup$
It is unfortunate you don't wish to use matrix rotations as that would be a relatively simple method to implement your aim. There exist users who are versed in the multivector geometric algebra... good luck.
$endgroup$
– James S. Cook
Dec 9 '18 at 5:51
$begingroup$
The point of this question is to understand how to use the wedge product. Using matrices is easy and there are numerous sources on how to use them. The sources I linked show that the wedge product can be used to rotate a 4D object. I want to understand how that is done exactly. I didn't know stack downvotes difficult questions now.
$endgroup$
– anon
Dec 9 '18 at 7:28
$begingroup$
I didn't downvote it. I hope Muphrid answers it for you.
$endgroup$
– James S. Cook
Dec 9 '18 at 22:26
add a comment |
$begingroup$
I'm trying to rotate a tesseract in 4D space for a project.
This shows I can use bivectors to "to generate rotations in four dimensions." Following exterior algebra and finding the wedge product, I've managed to get a 6D vector that supposedly describes my 4D rotation. This is great, except I have no idea how to use the 6D vector to rotate my 4D object.
I've looked at many links but none describe how to actually do the rotation using the wedge product. I'd like to stay away from matrix rotations.
- Rotating a 4 dimensional point?
- https://arxiv.org/pdf/1408.5799.pdf
- https://arxiv.org/pdf/1103.5263.pdf
- https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space
- https://en.wikipedia.org/wiki/Bivector#Four_dimensions
- http://eusebeia.dyndns.org/4d/vis/10-rot-1
How can I use the 6D vector to rotate the 4D object?
rotations exterior-algebra dimension-theory
asked Dec 9 '18 at 5:30
anonanon
6
$endgroup$
I'm trying to rotate a tesseract in 4D space for a project.
This shows I can use bivectors to "to generate rotations in four dimensions." Following exterior algebra and finding the wedge product, I've managed to get a 6D vector that supposedly describes my 4D rotation. This is great, except I have no idea how to use the 6D vector to rotate my 4D object.
I've looked at many links but none describe how to actually do the rotation using the wedge product. I'd like to stay away from matrix rotations.
- Rotating a 4 dimensional point?
- https://arxiv.org/pdf/1408.5799.pdf
- https://arxiv.org/pdf/1103.5263.pdf
- https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space
- https://en.wikipedia.org/wiki/Bivector#Four_dimensions
- http://eusebeia.dyndns.org/4d/vis/10-rot-1
How can I use the 6D vector to rotate the 4D object?
rotations exterior-algebra dimension-theory
rotations exterior-algebra dimension-theory
asked Dec 9 '18 at 5:30
anonanon
6
asked Dec 9 '18 at 5:30
anonanon
6
asked Dec 9 '18 at 5:30
anonanon
6
asked Dec 9 '18 at 5:30
anonanon
6
asked Dec 9 '18 at 5:30
anonanon
6
6
$begingroup$
It is unfortunate you don't wish to use matrix rotations as that would be a relatively simple method to implement your aim. There exist users who are versed in the multivector geometric algebra... good luck.
$endgroup$
– James S. Cook
Dec 9 '18 at 5:51
$begingroup$
The point of this question is to understand how to use the wedge product. Using matrices is easy and there are numerous sources on how to use them. The sources I linked show that the wedge product can be used to rotate a 4D object. I want to understand how that is done exactly. I didn't know stack downvotes difficult questions now.
$endgroup$
– anon
Dec 9 '18 at 7:28
$begingroup$
I didn't downvote it. I hope Muphrid answers it for you.
$endgroup$
– James S. Cook
Dec 9 '18 at 22:26
add a comment |
$begingroup$
It is unfortunate you don't wish to use matrix rotations as that would be a relatively simple method to implement your aim. There exist users who are versed in the multivector geometric algebra... good luck.
$endgroup$
– James S. Cook
Dec 9 '18 at 5:51
$begingroup$
The point of this question is to understand how to use the wedge product. Using matrices is easy and there are numerous sources on how to use them. The sources I linked show that the wedge product can be used to rotate a 4D object. I want to understand how that is done exactly. I didn't know stack downvotes difficult questions now.
$endgroup$
– anon
Dec 9 '18 at 7:28
$begingroup$
I didn't downvote it. I hope Muphrid answers it for you.
$endgroup$
– James S. Cook
Dec 9 '18 at 22:26
$begingroup$
It is unfortunate you don't wish to use matrix rotations as that would be a relatively simple method to implement your aim. There exist users who are versed in the multivector geometric algebra... good luck.
$endgroup$
– James S. Cook
Dec 9 '18 at 5:51
$begingroup$
It is unfortunate you don't wish to use matrix rotations as that would be a relatively simple method to implement your aim. There exist users who are versed in the multivector geometric algebra... good luck.
$endgroup$
– James S. Cook
Dec 9 '18 at 5:51
$begingroup$
The point of this question is to understand how to use the wedge product. Using matrices is easy and there are numerous sources on how to use them. The sources I linked show that the wedge product can be used to rotate a 4D object. I want to understand how that is done exactly. I didn't know stack downvotes difficult questions now.
$endgroup$
– anon
Dec 9 '18 at 7:28
$begingroup$
The point of this question is to understand how to use the wedge product. Using matrices is easy and there are numerous sources on how to use them. The sources I linked show that the wedge product can be used to rotate a 4D object. I want to understand how that is done exactly. I didn't know stack downvotes difficult questions now.
$endgroup$
– anon
Dec 9 '18 at 7:28
$begingroup$
I didn't downvote it. I hope Muphrid answers it for you.
$endgroup$
– James S. Cook
Dec 9 '18 at 22:26
$begingroup$
I didn't downvote it. I hope Muphrid answers it for you.
$endgroup$
– James S. Cook
Dec 9 '18 at 22:26
add a comment |
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$begingroup$
It is unfortunate you don't wish to use matrix rotations as that would be a relatively simple method to implement your aim. There exist users who are versed in the multivector geometric algebra... good luck.
$endgroup$
– James S. Cook
Dec 9 '18 at 5:51
$begingroup$
The point of this question is to understand how to use the wedge product. Using matrices is easy and there are numerous sources on how to use them. The sources I linked show that the wedge product can be used to rotate a 4D object. I want to understand how that is done exactly. I didn't know stack downvotes difficult questions now.
$endgroup$
– anon
Dec 9 '18 at 7:28
$begingroup$
I didn't downvote it. I hope Muphrid answers it for you.
$endgroup$
– James S. Cook
Dec 9 '18 at 22:26