steveh@emtek.UUCP (Steve Hollasch) (02/06/90)
I'm working on a master's thesis that incorporates the display of
4D objects. I've researched various articles in the computer graphics
world, but haven't come up with much besides the collection of 4D
visualization techniques that involve the display of the data as a 3D
object (e.g. marching cubes, cuberille, density emitters and the like.
I suspect that I'll be able to some find information in the math
sector. Could anybody give me references to information on this
subject?
My current plan is to view the data in 4D (with 4D light sources
and a 4D viewpoint), parallel project the object to 3D (does anybody
have a suggestion for another method of 4D --> 3D projection?), and
then apply regular visualization techniques to complete the imaging.
Another possibility is to bypass the 3D space and go directly from 4D
to 2D.
I also remember another poster that recently asked a similar
question (sorry, I've since lost track of your message).
_______________________________________________________________________________
Steve Hollasch [uunet!emtek!steveh] Tempe, Arizonasean@ms.uky.edu (Sean Casey) (02/07/90)
It would be *really* neat if you could display the object using some stereo glasses like the Haitek 3D LCD glasses costing about $120. So, anyone given some thought toward 4D raytracing???? Hmmmm? :-) Sean -- *** Sean Casey sean@ms.uky.edu, sean@ukma.bitnet, ukma!sean *** "May I take this opportunity of emphasizing that there is no cannibalism *** in the British Navy. Absolutely none, and when I say none, I mean there *** is a certain amount, more than we are prepared to admit." -MP
lmeyer@well.sf.ca.us (lhary meyer) (02/08/90)
Try projecting to stereoscopic 3D, I've got a SGI program that does a 4 or 5 demension (sic) cube into stereo. Real nice to what it spin!!
eugene@eos.UUCP (Eugene Miya) (02/09/90)
>Try projecting to stereoscopic 3D, I've got a SGI program that does a 4 or 5 >demension (sic) cube into stereo. Real nice to what it spin!! This isn't a flame on this poor fellow, but I've got an Iris 4D and I'll love to look at your program, but I seriously doubt you have a 4D cube. Prove me wrong with your software, send it to me, I love being proved wrong. It educates me. I learn, but I'm supposed to be a scientist, and that means being skeptical. I'd also be interested in knowing how you get a 5th Dimension without spinning a 60s record [Up Up and Away....] 8) Going back to the CACM paper which was noted in a posting some months ago, the authors from Bell Labs pointed out n>3 D has real problems in display. Their paper had the rotation of a tesseract (which I suspect you are doing). Lots of programs do this. But there are several issues: 1) tesseracts are PROJECTIONS of 4D hypercubes, they are not the cube itself. Most scientists need the Cube. Suppose I have a function f in Complex space C bar which I want to map the Complex space C bar. Well C bar consists of a real and imagery component-> 2 dimensions. Plotting the mapping can be 4-D! I also don't want |f(c)| (Euclidean distance of the function for 3-D. Now why would any one want to study such things? Hydrodynamics, particle physics, in my case to help a friend study gravitational lenses. 2) Cubes okay. I've other data. Points I want to plot, rays I wish to trace, etc. 3) DO NOT SUBSTITUTE TIME FOR A FOURTH PHYSICAL DIMENSION. Animation is a form of Blinn's Chi-Ting. (See why in 1). I might need time for something else like Time. 4) See the problem is we are plotting on 2-D surfaces. Our retinas are also 2-D. Let me illustrate a problem which computer screens and even stereo glasses will NEVER BE ABLE to solve. You can solve it with smart software, but see lack of understanding on the part of some computer people is why I go into my diatribes about the some of bogus people in scientific visualization. The problem is one of these hardest problems in mathematics: take a globe of the earth and "squash it" on a 2-D screen. So far it can't be done without compromising something: area, distance, etc. You see people ask for coordinates of the earth. Cute to look at basically (like the cube above) impractical for nearly everything else. A real 3-D globe can be used to determine distances between say NY and Tokyo (know what a great circle is?) which Mercator and other projections can't handle. Other solutions try to use color, and other qualitative cues: not great when you need the 4th D to be a spatial one. I've see attempts and I'm trying myself. You can't put a tape measure to a floating visual 3-D orbis, BUT you can do it in software. Guess how? I predict it will be with second generation graphics software developed for scientists to go beyond mere looking. But I still think graphics will never replace globes. Also fortunately we have the CAD folk working with the numerically controlled milling people. We have the cartographers who make maps. You trust your eyes too much when your eyes can be disceived. Meanwhile, I will hack and search for software. 8) Another gross generalization from --eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov resident cynic at the Rock of Ages Home for Retired Hackers: "You trust the `reply' command with all those different mailers out there?" "If my mail does not reach you, please accept my apology." {ncar,decwrl,hplabs,uunet}!ames!eugene Do you expect anything BUT generalizations on the net?
hollasch@enuxha.eas.asu.edu (Steve R. Hollasch) (02/10/90)
In article <6162@eos.UUCP>, eugene@eos.UUCP (Eugene Miya) writes: > >Try projecting to stereoscopic 3D, I've got a SGI program that does a 4 or 5 > >demension (sic) cube into stereo. Real nice to what it spin!! > > But there are several issues: > 1) tesseracts are PROJECTIONS of 4D hypercubes, they are not the cube itself. Granted, but you could also argue that an image of a normal 3D solid object is merely a projection, and not the object itself. What's the point? With the 3D object you can gain insight into clearance, structure and so on. More importantly (for me at least), you can spot trends, maximum regions, minimum regions, and the like. Heck, if you go backpacking, you don't disregard your topo map because it's not the true 3D object, do you? > 3) DO NOT SUBSTITUTE TIME FOR A FOURTH PHYSICAL DIMENSION ... I'm not. > 4) See the problem is we are plotting on 2-D surfaces. Our retinas are > also 2-D. Hmmmm. Are you arguing that the actual 3D object is not useful? > The problem is one of these hardest problems in mathematics: take a > globe of the earth and "squash it" on a 2-D screen. So far it can't > be done without compromising something: area, distance, etc. You > see people ask for coordinates of the earth. Cute to look at basically > (like the cube above) impractical for nearly everything else. A real > 3-D globe can be used to determine distances between say NY and Tokyo > (know what a great circle is?) which Mercator and other projections > can't handle. So, you project an image of the globe to the screen, and you now have before you a virtual 3D globe. Provide for user manipulation of this globe, and very soon (s)he'll be able to estimate relative sizes, distances, and the like. This is a good example of "bumping-up" a dimension to gain insight into the actual data. > But I still think graphics will never replace globes. I'm sure you've seen the dataglove & visual helmet combination pioneered by NASA as a means to model "real space". Why can't this as effective as walking around to a globe and rotating it? Or would our 2D retinas hold us up? =) > You trust your eyes too much when your eyes can be disceived. > Meanwhile, I will hack and search for software. 8) Eyes can be deceived quite easily, but they one of the best ways that humans have to rapidly and intuitively grasp many of the properties of objects, and to quickly isolate interesting regions. I will choose visual information over tactile or aural information (are you thinking of another method of perception?) almost every time.
tima@polari.UUCP (tim anderson) (02/10/90)
NURBS are generally thought of to reside in the fourth dimension. They get 'mapped' to 3d (then to 2d \grin) by some projective geometry. This, in turn, interpretes the '4th' coordinate as a pulling effect to the 'normal' 3D coordinates. I would hate to stick 'time' into the 4D to 3D NURBS mapping, because NURBS would look different depending on the clock speed of the CPU the program was currently running on. (This is a JOKE...) If I remember correctly, someone proved the existence of two 4th dimensions. This solution makes all of the Physicists happy, because they can say that time is the fourth dimension, and it makes the Mathematicians happy because they can say it isn't... tima@polari uw-beaver!sumax!polari!tima Place awesome signature here.
eugene@eos.UUCP (Eugene Miya) (02/10/90)
In article <487@enuxha.eas.asu.edu> hollasch@enuxha.eas.asu.edu (Steve R. Hollasch) writes: >In article <6162@eos.UUCP>, eugene@eos.UUCP (Eugene Miya) writes: >What's the point? With the 3D object you can gain insight into >clearance, structure and so on. More importantly (for me at least), >you can spot trends, maximum regions, minimum regions, and the like. >Heck, if you go backpacking, you don't disregard your topo map because >it's not the true 3D object, do you? I didn't say that. You can spot some trends, but your comment about manipulation is the key. You see a maximum, but display in science requires frames of reference, what is the max value, not just that it exists. You want value(max), or value(max), or |value(max)-value(min)|. And I certainly don't disregard topos especially those I drew. The problem with trends is the following: you can't simply predict something on the basis of solely using imagery. Given a ball at starting point A and ending point B, plot intermediate locations. You must assume something. Some naive artists will linearly interpolate, fine rolling on a flat surface. But suppose A is higher than B. Gravity changes non-linearly in position. You probably know the beautiful strobe photos (visualization) of Harold Edgerton, who recently died. I thought about writing an obituary for him. Muybridge who did the first photographic motion studies drew incredible flak from artists who thought they knew the way to portrary animals and people in motion. (He has a biography published by the UCa which shows how drawing changed.) Bottom line, you have to have additional information to predict or understanding trends. > So, you project an image of the globe to the screen, and you now >have before you a virtual 3D globe. Provide for user manipulation of >this globe, and very soon (s)he'll be able to estimate relative sizes, >distances, and the like. This is a good example of "bumping-up" a >dimension to gain insight into the actual data. My only comment is that the estimation is very bad. I would want the image software equivalent of a scale or ruler. Again more quantative info which visualization systems don't have but CAD systems do. > I'm sure you've seen the dataglove & visual helmet combination >pioneered by NASA as a means to model "real space". Why can't this as >effective as walking around to a globe and rotating it? Or would our >2D retinas hold us up? =) Yes, Scott and Mike's lab is just over in another building. This brings and important issue: using the real world to work with images. On a screen I can hold a ruler/scale up. No good its a rendering of a 3-D object (right?). Can't do it easily with stereo systems. You have your virtual globe in the middle of the room, what mechanism can one place a the tape measure in my pocket to measure distance? > Eyes can be deceived quite easily, but they one of the best ways >that humans have to rapidly and intuitively grasp many of the >properties of objects, and to quickly isolate interesting regions. I >will choose visual information over tactile or aural information (are >you thinking of another method of perception?) almost every time. Sure. No one will disagree, but that's why we have microscopes, telescope, lenses, Gieger counters, and whole slews of scientific instruments. Bottom line: visualization just does not go far enough. Anyways basically good points. Another gross generalization from --eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov resident cynic at the Rock of Ages Home for Retired Hackers: "You trust the `reply' command with all those different mailers out there?" "If my mail does not reach you, please accept my apology." {ncar,decwrl,hplabs,uunet}!ames!eugene Do you expect anything BUT generalizations on the net?
sean@ms.uky.edu (Sean Casey) (02/11/90)
eugene@eos.UUCP (Eugene Miya) writes: |Sure. No one will disagree, but that's why we have microscopes, telescope, |lenses, Gieger counters, and whole slews of scientific instruments. |Bottom line: visualization just does not go far enough. Ultimately, we may be able to expand our ability to visualize in more than the usual 2 or 3 dimensions. Imagine in the future a child using a direct brain input device. Much like someone learning two languages from childhood, it may be possible to adapt the brain to seeing (read: perceiving) in ways we can't now understand. Sean -- *** Sean Casey sean@ms.uky.edu, sean@ukma.bitnet, ukma!sean *** "May I take this opportunity of emphasizing that there is no cannibalism *** in the British Navy. Absolutely none, and when I say none, I mean there *** is a certain amount, more than we are prepared to admit." -MP
doug@xdos.UUCP (Doug Merritt) (02/11/90)
This stuff is really the domain of sci.physics, but it has been *thoroughly* hashed and rehashed over there, so I don't think that it is appropriate to move the discussion. But it also does not directly concern graphics, so most of you will want to skip the following! Feel free to criticize the following all you like, but I suggest that email would be the best way to do so, rather than cluttering comp.graphics with non-graphics stuff. In article <1263@polari.UUCP> tima@polari (tim anderson) writes: > >If I remember correctly, someone proved the existence of two 4th dimensions. >This solution makes all of the Physicists happy, because they can say that >time is the fourth dimension, and it makes the Mathematicians happy because >they can say it isn't... Phrased this way, this is pretty much meaningless. To laymen, a "dimension" always means "a spatial dimension that's part of our universe such as up/down, right/left etc". In both math & physics, however, the term just refers to how many variables you've got in an equation. If the equation happens to refer to space (volume), for instance a Euclidean equation of distance d = sqrt(x^2 + y^2 +z^2), then these three dimensions are the intuitive sort. But the variables (same as dimensions, remember) could just as well be referring to color, day of the week, and the reader's birthday. Or to nothing in particular...in pure math it is the relationships that are of interest, and no particular mapping between the variables and anything in the real world is assumed. In applied math, some particular abstract set of relationships developed in the realm of pure math may often be applied to any one of many totally different kinds of physical phenomena. In terms of relativity, it's true that there are four dimensions assumed, three of which are nominally considered to be "space-like" and the fourth of which is (again nominally) "time-like". So there are nominally only three spatial dimensions even in relativistic physics. Of course, it turns out that at relativistic speeds, that fourth dimension can appear space-like, loosely speaking. Which just means that the naive definition of dimension is misleading. Still, space-time can be visualized geometrically as a 4 dimensional space. It's not a Euclidean space, though, so intuition tends to give the wrong answers. And one of those dimensions has different properties than the others...the distance formula is sqrt(x^2 + y^2 + z^2 - t^2), and the change in sign for the time dimension gives that dimension different geometric properties than the three space-like dimension. This is further complicated by the fact that any given object always has a constant velocity of C (speed of light) in four-space. An object apparently at rest has a velocity of C along the time axis. "Accellerating" that object actually has the effect of rotating its trajectory away from the time axis, and toward one of the spatial axis, lessening its velocity component in the time dimension and increasing it in a spatial dimension. Light itself always has a component of zero along the time axis, and so its velocity of C is always apparent purely in the spatial dimensions. The various bizarre and well publicized relativistic effects of high speed travel are not present in the reference frame of the object itself. They are visible only to an outside observer, whose time dimension is pointing in a different direction in four space...the two systems have different metrics of time, which causes various measurements to behave non-intuitively. There have been other geometric models for space time that have been proposed that add still more dimensions. Although these other dimensions can be visualized as space-like in an abstract geometric sense, they do not manifest themselves *macroscopically* (i.e. in intuitive terms) as space-like. There continues to be questions of exactly what we mean by "space" and "time" and what that may have to do with the geometric structure of the universe, and these questions are by no means completely resolved. Back to the original point: although it may sound impressive to declare that "time is the fourth dimension" (or like the graffiti in Berkeley, "gravity is the fifth dimension :-), this is more misleading than anything. A more neutral phrasing is that "time is *a* fourth dimension", because then it's more clear that it's just an arbitrary variable. You could say the same thing about mass or charge or color or whatever...they could all be *a* fourth dimension in some system of equations. Doug -- Doug Merritt {pyramid,apple}!xdos!doug Member, Crusaders for a Better Tomorrow Professional Wildeyed Visionary
leech@cassatt.cs.unc.edu (Jonathan Leech) (02/11/90)
In article <6174@eos.UUCP> eugene@eos.UUCP (Eugene Miya) writes: >This brings and important issue: using the real world to work with >images. On a screen I can hold a ruler/scale up. No good its a >rendering of a 3-D object (right?). Can't do it easily with stereo systems. >You have your virtual globe in the middle of the room, what mechanism >can one place a the tape measure in my pocket to measure distance? Use a virtual measuring tape, of course (no :-) here). Or, more generally, a mechanism for finding and characterizing geodesics on the object you're inspecting. -- Jon Leech (leech@cs.unc.edu) __@/ "Enhanced 386... Runs Unit, Zenix, 0s/s & DOS..." - Competitive Computer Components Ad, Computer Shopper 1/89
hollasch@enuxha.eas.asu.edu (Steve R. Hollasch) (02/11/90)
> ... You see a maximum, but display in science > requires frames of reference, what is the max value, not just that it exists. > You want value(max), or value(max), or |value(max)-value(min)|. > > The problem with trends is the following: you can't simply predict > something on the basis of solely using imagery. ... > > Bottom line, you have to have additional information to predict or > understanding trends. > > Bottom line: visualization just does not go far enough. I think I better understand your viewpoint; it seems that you oppose visualization as the endpoint in data analysis. For the most part, I agree with you -- visualization does not allow you to make accurate predictions about the nature of the data, nor does it allow you to predict the response to external conditions. For the most part, visualization is the beginning of serious data analysis -- it allows you to quickly spot "interesting" regions for further analysis. However, I think that there ARE exceptions to this view. In some cases visualization is the final analysis of a set of data. Consider, for example, the fact that not all higher-dimensional data are based on a particular 3D space with associated scalar (or vector) values. One great example of this is the use of visualization to map upper derivatives of mathematical functions. Doctor Farin, a professor here who specializes in CAGD, has recently published a book on this subject that has some very interesting pictures of mathematically- defined (B-spline and the like) surfaces. The images, however, are based on the C2 properties of this surface, not on the physical view of the surface itself. The end result is such that poor knot selection (easily with an error of .1 mm on an automobile hood) can produce C2 oscillations that would otherwise not be noticable, even if you had the hood in front of you (although some VERY experienced people can look at reflections of the hood and tell that its C2 properties are not too slick). These sorts of applications really benefit from visualization. It is easy to think of these sorts of applications that extend to hyperspace and further. In this respect, visualization is definitely useful because it has no base in the "real" world.
kmaier@p3.f11.n369.z1.FIDONET.ORG (Kenneth Maier) (02/12/90)
To: lmeyer@well.sf.ca.us >From: lmeyer@well.sf.ca.us (lhary meyer) >Date: 8 Feb 90 06:59:54 GMT >Organization: Whole Earth 'Lectronic Link, Sausalito, CA >Message-ID: <16033@well.sf.ca.us> >Newsgroups: comp.graphics > >Try projecting to stereoscopic 3D, I've got a SGI program that does a 4 >or 5 >demension (sic) cube into stereo. Real nice to what it spin!! Is is possible for you to post more information regarding this stereoscopic package? (ie.. FTP site or something...) I have a program for the PC that runs under EGA/VGA which does "3D" if you have those "old" red and blue cardboard glasses that they used to give away at 7-Eleven. (called ANAGLYPH.EXE) Lets you design your own wire-frame object and then spins it for you. Really neat effect for the PC. A little too slow for my standards if you want to have a large image...Have to re-write it when I get the CRAY set-up in my living room. <grin> -Kenneth -- Kenneth Maier via FidoNet node 1:369/11 UUCP: {attctc,<internet>!mthvax}!ankh,novavax!branch!11.3!kmaier
mitchell@cbmvax.commodore.com (Fred Mitchell - Product Assurance) (02/14/90)
In article <14094@s.ms.uky.edu> sean@ms.uky.edu (Sean Casey) writes: >Ultimately, we may be able to expand our ability to visualize in more than >the usual 2 or 3 dimensions. Imagine in the future a child using a direct >brain input device. Much like someone learning two languages from childhood, >it may be possible to adapt the brain to seeing (read: perceiving) in ways >we can't now understand. The problem with 4-D visualization is this: To visualize the 4th dimension PROPERLY would require a pair of 4th-dimensional eyes, each bearing a 3-D retina (in contrast to our 3-D eyes with 2-D retinas). The brain, of course, would be wired to handle such. Also note that a 3-D retina would involve a million-fold increase in the volume of data that must be processed by this 4-D brain. I'm not saying the task is impossible (I've been trying for years to improve my 4-D visualization [which led to the above observation]). It is just that the task is inherently more complicated than one would suspect. Whether OUR brains can handle imagining something properly that would require such an enormous increase in bandwidth is open to debate. For sure we can grasp some primitive elements of the 4th dimension (as I have done), but to TRULY visualize it as well as we do the 3rd dimension? I submit that that would require a MUCH bigger brain! To give you an idea of the 'wierdness' of it, A 4th-dimensional creature looking upon one of us 3rd-dimensional beings would see EVERY PART of us simultaneously- skin, gut, heart, blood, brain, bones, EVERYTHING! We would appear "ugly" and "unappealing" (assuming that they have the same asthetics as we do), as well as just plain "flat" (in their sense, not ours!). They would also be able to hold an infinite number of us in the palm of their 4th-dimensional "hands" (assuming their "hands" are the same length as our bodies). Somehow this sounds Twilight-Zonish! :-) >Sean -Mitchell mitchell@cbmvax.UUCP "To Life, Immortal."
gcrum@koh-sun3.usc.edu (Gary Crum) (02/14/90)
At the 1988 Computer Graphics Symposium in Ft. Collins CO presented by Hewlett-Packard, Cliff Beshers (beshers@cs.columbia.edu) demonstrated "Interactive 4D animation". He displayed the 2D projection of a 4D cube being manipulated in real time. The manipulation included rotation about 4 basis axes, but no translation, mind you -- coordinates were run through the transform pipeline of an HP Turbo-SRX twice in order to do the 4D->3D->2D projection, and since the hardware supports 4x4 but not 5x5 matrices... Shading was used to help the visualization, I recall. Also demonstrated was "Ray-tracing with polarization" by David Kurlander and Larry Wolff. They and Cliff Beshers are apparently students of Steven Feiner (feiner@cs.columbia.edu), who presented "Knowledge-based graphical interface design" at the symposium. I don't see any papers about the demos in my proceedings. They were both fascinating demonstrations of things I and I'm sure many others have thought about. My question for them was "Have you considered doing 4D ray-tracing with polarization?" :-) Gary
lmeyer@well.sf.ca.us (lhary meyer) (02/15/90)
I am not at an Internet site, so no FTP. Also I am VP of Stereographics Corp. and have a commercial involvement with stereo display. P}ilease EMail me for further info on software, manuals, hardware as it is improper to post commercial diatribes!
prem@geomag.fsu.edu (Prem Subrahmanyam) (02/16/90)
Along the lines of "seeing" the fourth dimension, can anyone
recommend a really good book that can help in understanding
the mathematics of mapping from the 4th to the 3rd dimension,
i.e., mapping of hypercubes to 3-d space and from there to a
2-d display screen, or going directly from 4 to 2-d. I
understand that Flatland is good for teasing the mind with some
fourth dimensional concepts, but I would like a little more.
---Prem Subrahmanyammitchell@cbmvax.commodore.com (Fred Mitchell - Product Assurance) (02/17/90)
In article <512@fsu.scri.fsu.edu> prem@geomag.UUCP (Prem Subrahmanyam) writes: > > Along the lines of "seeing" the fourth dimension, can anyone > recommend a really good book that can help in understanding > the mathematics of mapping from the 4th to the 3rd dimension, > i.e., mapping of hypercubes to 3-d space and from there to a > 2-d display screen, or going directly from 4 to 2-d. I > understand that Flatland is good for teasing the mind with some > fourth dimensional concepts, but I would like a little more. > ---Prem Subrahmanyam Yes. EXPERIMENTS IN 4 DIMENSIONS by David Heiserman. -Mitchell