Four (spatial) dimensional representation with S3D - Has it been done? 4D models, tools, visualisati
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I saw another topic about this but it had no replies so I thought I might return the idea to the table.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain [i]experience[/i] in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
I saw another topic about this but it had no replies so I thought I might return the idea to the table.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain experience in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
I saw another topic about this but it had no replies so I thought I might return the idea to the table.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain [i]experience[/i] in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
I saw another topic about this but it had no replies so I thought I might return the idea to the table.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain experience in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
[quote name='cybereality' date='14 June 2011 - 04:22 AM' timestamp='1308018179' post='1251435']
Do you have a picture of something that is 4D? I'm not sure I understand.
[/quote]What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[quote name='cybereality' date='14 June 2011 - 04:22 AM' timestamp='1308018179' post='1251435']
Do you have a picture of something that is 4D? I'm not sure I understand.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[quote name='cybereality' date='14 June 2011 - 04:22 AM' timestamp='1308018179' post='1251435']
Do you have a picture of something that is 4D? I'm not sure I understand.
[/quote]What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[quote name='cybereality' date='14 June 2011 - 04:22 AM' timestamp='1308018179' post='1251435']
Do you have a picture of something that is 4D? I'm not sure I understand.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[quote name='crim3' date='14 June 2011 - 12:33 PM' timestamp='1308051229' post='1251582']
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[/quote]
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
[quote name='crim3' date='14 June 2011 - 12:33 PM' timestamp='1308051229' post='1251582']
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
[quote name='crim3' date='14 June 2011 - 12:33 PM' timestamp='1308051229' post='1251582']
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[/quote]
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
[quote name='crim3' date='14 June 2011 - 12:33 PM' timestamp='1308051229' post='1251582']
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
Ok I have no idea what those stairs have to do with 4D. Ignore that.
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: [url="http://www.youtube.com/watch?v=t-WyreE9ZkI"]http://www.youtube.com/watch?v=t-WyreE9ZkI[/url]
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method [url="http://dogfeathers.com/java/hypercube2-nogl.html"]http://dogfeathers.com/java/hypercube2-nogl.html[/url]
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Ok I have no idea what those stairs have to do with 4D. Ignore that.
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: " rel="nofollow" target = "_blank">
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method http://dogfeathers.com/java/hypercube2-nogl.html
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Ok I have no idea what those stairs have to do with 4D. Ignore that.
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: [url="http://www.youtube.com/watch?v=t-WyreE9ZkI"]http://www.youtube.com/watch?v=t-WyreE9ZkI[/url]
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method [url="http://dogfeathers.com/java/hypercube2-nogl.html"]http://dogfeathers.com/java/hypercube2-nogl.html[/url]
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Ok I have no idea what those stairs have to do with 4D. Ignore that.
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: " rel="nofollow" target = "_blank">
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method http://dogfeathers.com/java/hypercube2-nogl.html
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain [i]experience[/i] in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain experience in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain [i]experience[/i] in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
Four (or any number of) spatial dimensions, as some may know, are theoretically possible. Of course, we do not know if there is a fourth dimension, but whether it be for research, for mental exercise, artistic/aesthetic interest or just plain old fun, there are many people who like to think about what four dimensions would look like, what goes on in such a "world" and just delve right into the topic.
Most of the discourse revolves around discussion, maths and mental exercises. There have been ways to visually illustrate four dimensional shapes for a long time, and many programs too. Without going into too much detail, all the illustrations so far have been extremely limited due to the fact that we can only represent them in 2D. That is 2 less dimensions and is the equivalent of trying to somehow represent a whole cube on a straight line.
Stereoscopic images of four dimensional shapes have been done, however, using the cross-eye or wall-eye methods. These are painful and highly limited, of course, but they do add another pseudo-dimension that reduces quite a bit of ambiguity in the representation. The ability to rotate them reduces more ambiguity and an excellent program that allows you to do both, with much flexibility is Stella4D.
We have the technology now (and have had it for a while!) to really expand on this with 3D vision. Those who want to actually gain an intuitive grasp of 4D will be greatly aided by real immersion and this is now possible with S3D. With S3D, we can have n-1 dimensional representation (almost, seeing as we are stuck on one side of our screen), and that would be the equivalent of representing a cube on paper, which we do all the time!
I am amazed that there are no programs that do this, but the community for people interested in 4D is obviously very small. If there are any, please let me know. If you share interest in this and have any ideas or know anything at all about the connection between 4D and S3D, please share it here.
If something is done, and done properly, we can actually gain experience in dealing with four spatial dimensions, and we will have accessed our minds to a world that is has as many more possibilities that 3D has over 2D! Who knows, perhaps even games can be made that allow us to go to that world and those of the human race that have interest and ambition can let their imagination experience something higher, and better, than...well everything we know.
check my blog - cybereality.com
check my blog - cybereality.com
http://www.optical-illusion-pictures.com/images/stairs.jpg[img]http://www.optical-illusion-pictures.com/images/stairs.jpg[/img]
[/quote]
Hmmm....reminds me of the 80's arcade game Crystal Castles.
On a side note - MC Escher was painting in 4D?
http://www.optical-illusion-pictures.com/images/stairs.jpg
Hmmm....reminds me of the 80's arcade game Crystal Castles.
On a side note - MC Escher was painting in 4D?
http://www.optical-illusion-pictures.com/images/stairs.jpg[img]http://www.optical-illusion-pictures.com/images/stairs.jpg[/img]
[/quote]
Hmmm....reminds me of the 80's arcade game Crystal Castles.
On a side note - MC Escher was painting in 4D?
http://www.optical-illusion-pictures.com/images/stairs.jpg
Hmmm....reminds me of the 80's arcade game Crystal Castles.
On a side note - MC Escher was painting in 4D?
Do you have a picture of something that is 4D? I'm not sure I understand.
[/quote]What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
Do you have a picture of something that is 4D? I'm not sure I understand.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
Do you have a picture of something that is 4D? I'm not sure I understand.
[/quote]What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
Do you have a picture of something that is 4D? I'm not sure I understand.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
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I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
[/quote]
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
What can be represented is a 2D projection of a 3D projection of a 4D object. If you search, you'll find some java applets that render hypercubes (4D cube) and other geometric forms. You can even find variations of the Rubik's cube with more than 3 dimensions for the most advanced fanatics.
The idea of the OP is to have a stereoscopic representation of that 3D projection of a 4D object.
I'm not sure it would work in stereo myself. I mean, imagine those stairs, or a cube, how would it determine which parts to render at which depths? It isn't going to know which bit you are looking at and alter its depth accordingly, technically the stairs should go up (or down) indefinately, and whereas we can represent that as a 2D drawing or a 2D representation of a 3D model of a 4D model (lol), the depth part of Stereo isn't going to manage it sadly.
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: [url="http://www.youtube.com/watch?v=t-WyreE9ZkI"]http://www.youtube.com/watch?v=t-WyreE9ZkI[/url]
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method [url="http://dogfeathers.com/java/hypercube2-nogl.html"]http://dogfeathers.com/java/hypercube2-nogl.html[/url]
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: " rel="nofollow" target = "_blank">
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method http://dogfeathers.com/java/hypercube2-nogl.html
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: [url="http://www.youtube.com/watch?v=t-WyreE9ZkI"]http://www.youtube.com/watch?v=t-WyreE9ZkI[/url]
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method [url="http://dogfeathers.com/java/hypercube2-nogl.html"]http://dogfeathers.com/java/hypercube2-nogl.html[/url]
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
Let's put it this way. Just as a 3D shadow is 2D, so to a 4D "shadow" would be 3D. Thus a 4D "cube" (called a tesseract, or a 4D hypercube) would give a 3D shadow that would look something like this: " rel="nofollow" target = "_blank">
It is really hard to get and I am not expecting anyone to unless they have much experience in the subject, but having that video, but a 3D stereoscopic version of it, would greatly aid in comprehending it. Here is an example using the cross-eye method http://dogfeathers.com/java/hypercube2-nogl.html
The depth to be rendered would be the depth it would have if it were actually in a 3D space. This is not something ambiguous and is perfectly possible.
I am not saying we can render actual 4D shapes, we haven't the room in our universe to contain them. But we can make an accurate representation of their "shadows" with stereoscopy and then it would be an equivalent problem to the problem of explaining a cube to a 2D being with drawings. Not saying that's easy, but who ever said easy was the only way to have fun?
There's one at http://tesseract-trainer.soft32.com/ but the dang thing is in OpenGL.
There's one at http://tesseract-trainer.soft32.com/ but the dang thing is in OpenGL.