----------------------------------- Catalyst Thu Nov 18, 2004 11:07 pm 4-Dimensional Projection ----------------------------------- An idea I had that I wanted to toy around with (used Turing since it was fast to prototype) Left Click to rotate the tesseract (4-d cube) and Right Click to rotate the resulting 3 dimensional projection of the tesseract. note: The rotation in 4 dimensions might be a bit off since I didnt have any source material on the topic ----------------------------------- Neo Thu Nov 18, 2004 11:59 pm ----------------------------------- Thats simply amazing man... How do you even get started doing these kinds of programs? I mean where do you learn this stuff? ----------------------------------- Neo Fri Nov 19, 2004 12:11 am ----------------------------------- If you change line 232 from drawline to drawmapleleaf you get a really cool effect. 8) ----------------------------------- Tony Fri Nov 19, 2004 12:30 am ----------------------------------- alright, more cool stuff from Catalyst! hmm... watching the hypercube movie is not helping me understand as to what's going on :? ----------------------------------- zomg Fri Nov 19, 2004 11:01 am ----------------------------------- this is pretty wicked i love how its smoth and the shadows make it look friggen wicked nice job!! :D :D ----------------------------------- Andy Fri Nov 19, 2004 3:47 pm ----------------------------------- nicely done... where r u applyin for uni btw and what program ----------------------------------- Delos Fri Nov 19, 2004 4:40 pm ----------------------------------- Argh! 4th dim visualizations... You know Catalyst, this stuff is really cerebrally challenging. Don't they use these sorts of things to model really complex network topologies or something...? ----------------------------------- rizzix Fri Nov 19, 2004 11:39 pm ----------------------------------- think of a box composed with each side a box.. that is ur hypercube... nice work btw. ----------------------------------- Paul Fri Nov 19, 2004 11:58 pm ----------------------------------- explain a four dimensional object to me please. I couldn't figure head or tail out of that. ----------------------------------- zomg Sat Nov 20, 2004 12:01 am ----------------------------------- u have to click the mouse and move the cube EDIT: Ithought he didnt know how to use the program... My bad :oops: ----------------------------------- Tony Sat Nov 20, 2004 3:02 am ----------------------------------- explain a four dimensional object to me please. well mathematically its really easy. Instead of (x,y,z) coordinate system we use to decrible object's potition we use (x,y,z,w) (not sure on the name of 4th element). Visually/Conseptually though... Think of it this way. You have a some dimention. To go to the step above, you translate the shape in the direction perpendicular to itself and join the edges. 1D ___ line 2D |___ another 1D line perpendicular to the first line. Join the edges to get a square http://www.mathematische-basteleien.de/hyper01.gif you follow the same pattern to get to 4D. Just draw a cube perpendicular to itself, so that each face of the hypercube is a cube (similary as each face of a cube is a square and each edge of a square is a line) ~ thus 4D. http://www.mathematische-basteleien.de/hyper07.gif Go [url=http://www.mathematische-basteleien.de/hypercube.htm]here for further explanation ----------------------------------- Paul Sat Nov 20, 2004 1:00 pm ----------------------------------- I see, my bad. I got kinda mixed up between this and my reading in string theory and calabi-yau spaces. A hypercube does not actually represent extra spacial dimensions does it? :? ----------------------------------- MihaiG Sat Nov 20, 2004 1:44 pm ----------------------------------- that hyper cube really made me think... for the first time my mind went blank..... thnx.... now forgot what i was going to say ;-)...btw splendid good job old chap ----------------------------------- MihaiG Sat Nov 20, 2004 1:53 pm ----------------------------------- im sorry i just made a 5-Dimmesional cube ----!!! instead of drawline.... put drawbox!!! or a hyper oval... out drawoval.... or hyperstar...drawstar!!! the 5dcube is crazy shit(sorry for postiong twice i didnt mean it) ----------------------------------- HyperFlexed Sat Nov 20, 2004 1:57 pm ----------------------------------- It's still 3d though. In visual. I'm assuming 4d is only theoretic. I still don't get it. ----------------------------------- rizzix Sat Nov 20, 2004 4:30 pm ----------------------------------- do u know how a cube has 6 2D sides? a hypercube has 6 3D sides(i.e each side has a depth dimension as well).. hence 4D.. cuz to describe the cube u have to talk about 4 different dimensions ----------------------------------- Catalyst Sat Nov 20, 2004 4:34 pm ----------------------------------- dodge: thinking science or engineering but having a hard time deciding past that, uni will probably waterloo or mcmaster (since it has general 1st year engineering) hyperflexed: yes in visual it is only 3d since im projecting the 4d cube into 3d space just as you project a 3d object to 2d to get an image of a 3d dimensional object on a screen some of the projection attributes might be distorting was going on here, this version give a better view (also replaced 1st one too) ----------------------------------- HyperFlexed Sat Nov 20, 2004 9:01 pm ----------------------------------- okayy... I thought I was going crazy. good. ----------------------------------- Andy Sun Nov 21, 2004 8:06 pm ----------------------------------- cool.. what engineering? im prolly doing either software engineering or computer... ----------------------------------- Catalyst Sun Nov 21, 2004 9:50 pm ----------------------------------- undecided myself ----------------------------------- RaPsCaLLioN Mon Nov 22, 2004 9:31 pm ----------------------------------- Not all 3D objects are defined as a perpendicular translation of a 2D shape though. Such as a sphere is a two plane rotation of a circle mapping each point along the circumfrence as it spins - think of a spinning quarter, it looks like a sphere as it spins. How would you represent a 4D circular shape? ----------------------------------- rizzix Mon Nov 22, 2004 10:44 pm ----------------------------------- 4D circular... himm like a tire? ah! has to be.. ----------------------------------- RaPsCaLLioN Mon Nov 22, 2004 11:01 pm ----------------------------------- Uh... 4D spherical maybe? See each shape has it's own name in whatever dimension. Square=Cube=Tesseract... but Circle=Sphere=? How would you represent a rounded 4D image? What would you call it? ----------------------------------- Catalyst Mon Nov 22, 2004 11:45 pm ----------------------------------- im guessing it would look exactly like a sphere (making it rather uninteresting) when projected down to 3d(since spheres are circles when projected to 2d). To generate it you would need to rotate a sphere through the 4th dimension. For naming it i think hypersphere would work although it lacks pinache. :lol: ----------------------------------- Viper Thu Nov 25, 2004 4:48 pm ----------------------------------- omg that is sooo sick ----------------------------------- omar Wed Dec 01, 2004 8:54 am ----------------------------------- True it's not 4D but it is still pretty amazing... with drawstar and drawmapleleaf u will be pretty much stuned ( hey snowman guy make ur avatar smaller ... it's annoying.) ----------------------------------- zomg Wed Dec 01, 2004 11:55 am ----------------------------------- i always thought a sphere was just 2d circle with shading to make it look like its 3d how could u make a 4d circle :? unless it was transparent i guess... ----------------------------------- m&m Wed Dec 01, 2004 12:08 pm ----------------------------------- this is pretty mind boggling :wall: jeez i didn't evenkno anything existed beyond 3D lol ----------------------------------- rizzix Wed Dec 01, 2004 3:10 pm ----------------------------------- yes there is also 5d 6d 7d 8d and Nd... but u may not be able to represent them visually ----------------------------------- omar Thu Dec 02, 2004 9:41 am ----------------------------------- Ok listen professors all over the world have concluded that we live in a three dimensional world hence the fact that any figure you can imagine be defined by three axis... the only other argument is that the fourth dimension is time which is still unreasonable to my standards. If you claim you have a four dimensional object it can still be defined using the three axis x,y,z don't be stupid :evil: ----------------------------------- rizzix Thu Dec 02, 2004 4:07 pm ----------------------------------- just because u can't imagine a 4th axis dosen't mean its not there. sheesh. the same goes for an Nth axis. ----------------------------------- MihaiG Thu Dec 02, 2004 8:45 pm ----------------------------------- string teory tells us that there can be up to 9-dimensions but some can be so small that we can't see them or feel them... some axis might come up when reaching speeds near C(speed of light in vacum, 186,000m/h)... also studies show that the universe is shaped like a doughnut.... imagine a piece of paper.... connect two of the oppopsite sides togagher... this tell us that if we go of one edge we will reapear on the other... you chould have a tube.. now connect the other opposite sides.... of the tube and you will get a doughnut.... therfore... if you were to go on off one edge you would reapear on the opposite side.... scientist now believe the universe is finite.... they think were the only galaxy and when we look out were seeing different views of our galaxy... like if your in between to panes of mirrors.. you see infinite selves..... i hope his helped some of youze... some how credits go to Stephen Hawking for his contribution to science... "The universe in a nutshell" ----------------------------------- Paul Thu Dec 02, 2004 10:08 pm ----------------------------------- Actually recent research show that strings may need 10 dimensions, the 9 dimensions was just an estimate. The hidden dimensions are small, and are described as "curled up". Eg. Viewing a garden hose from a distance, one may describe it as being 1 dimensional, to describe the position of anything on the garden hose, you only need to give the left or right position. Upon closer examination, one sees the garden hose actually has another 'curled up' dimension, and now to describe the position of an object on its surface, you'd need to give horizontal coordinates AND its position on the curled up dimension. The specific shapes of the 'curled up' dimensions are not known. 2 dimensions can be curled up to a sphere shape, or a donut shape. As for the universe being a donut shape, I've never heard of that. But research shows that 6 dimensions can be 'curled up' into something called a calabi-yau space, or calabi-yau shape. But thats complex math that is beyond me. Here's a 2D image trying to represent the 6 dimensional calabi-yau space http://people.cs.uchicago.edu/~mbw/astro18200/calabi-yau-space3.jpg ----------------------------------- Jonny Tight Lips Mon Dec 13, 2004 8:25 pm ----------------------------------- WOW! I've been trying for weeks just to get a 3D cube to rotate. Man I feel stupid now. Well I will keep trying. That is some amazing stuff. wow. I am just so blown away :shock: . Great job! I know I may be asking a lot but would it be possible for someone to comment that code so that I may be able to understand it a little better? It would an amazing help to me if you could. Thanx ----------------------------------- endusto Tue Feb 15, 2005 9:03 pm ----------------------------------- i dont get it, all i see is a cube inside a cube ----------------------------------- Drakain Zeil Wed Feb 16, 2005 3:33 pm ----------------------------------- Ok listen professors all over the world have concluded that we live in a three dimensional world hence the fact that any figure you can imagine be defined by three axis... the only other argument is that the fourth dimension is time which is still unreasonable to my standards. If you claim you have a four dimensional object it can still be defined using the three axis x,y,z don't be stupid :evil: They do? http://www.pbs.org/wgbh/nova/elegant/dimensions.html http://www.wwnorton.com/catalog/fall03/005858.htm http://interactions.org/quantumuniverse/questions/q3.html http://superstringtheory.com/ http://www.fortunecity.com/emachines/e11/86/dimens.html http://www.boston.com/ae/books/articles/2004/03/21/the_wonders_of_an_11_dimensional_universe/ http://www.bun.kyoto-u.ac.jp/~suchii/Einstein/generalcoord.html Interesting. ----------------------------------- cycro1234 Wed Feb 16, 2005 7:56 pm ----------------------------------- That's crazy! The multiple dimensions thing. What if aliens live in the 6th dimesion, and one day when scientists figure out that aliens have been with us for billions of years, every1 will freak. :shock: I am so getting those universe books. What if I discover the next dimesions?? OMG.... ----------------------------------- Drakain Zeil Wed Feb 16, 2005 8:40 pm ----------------------------------- ... Oh boy as long as you never read "The bigest secret" I'll die a happy man. (about 4-dimensional alien invaders that have invaded our world since the begining of time... some nut job conspiracy about lizardmen).