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Topic: hyperspace transformation (Read 536 times) |
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st33d
 
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hyperspace transformation
« on: Feb 15th, 2005, 4:26pm » |
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I'm unaware as to how Processing transforms the z co-ordinate into a perspective image. I'm assuming there's just some kind of shrink or magnify operation. Now however I need to plot in a fourth dimension.
I've made a series of particle experiments base on the light cycles of the film and game Tron. They always turn right. For 3 dimensions I just adapted the principle using the pattern in the co-ordinate movements. I then figured out the same pattern should work in four or even five dimensions. So I mapped out a time cube, and a cube with parallel dimensions.
3D
http://www.st33d.net/processing/liteDark6.html
4D
http://www.st33d.net/processing/liteDark10.html
5D
http://www.st33d.net/processing/liteDark11.html
However, there is also the concept of the hypercube. Where one maps four dimensions into a three dimensional or two dimensional view.
http://www.maa.org/editorial/knot/tesseract.html
My code with the time cycles already tracks movement in four dimensions, but it displays it as the passage of time. I'm trying to figure out now how to map the trails in a hypercube.
Does anyone know of any examples of hyperspace transformation algorithm? And perhaps some straight forward methods of drawing a hypercube?
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I could murder a pint.
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5cameron
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Re: hyperspace transformation
« Reply #1 on: Feb 25th, 2005, 1:36am » |
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sorry i can't help with the question, but thanks for the interesting reading!
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st33d
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Re: hyperspace transformation
« Reply #2 on: Feb 25th, 2005, 6:41pm » |
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I've mapped the hypercube now. I took the easy option of a cube in a cube. I'll figure out rotation once I've finished learning the assembley and C I need to know to power my robot. Right now I know nothing.
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I could murder a pint.
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fry
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Re: hyperspace transformation
« Reply #3 on: Feb 25th, 2005, 7:09pm » |
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here's an old sketch i did with code that shows you how to do the 4D stuff, which is then easily ported up to 5+ dimensions:
http://acg.media.mit.edu/people/fry/atmosphere/ndim/
more details on that page.
n-dimensional geometry is fun stuff, a bit mind-bending after a bit...
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| « Last Edit: Feb 25th, 2005, 7:10pm by fry » |
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st33d
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Re: hyperspace transformation
« Reply #4 on: Feb 25th, 2005, 8:38pm » |
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Magic. I'll admit my brain is too fried from trying to understand machine code right now to try out some hyperspace rotation (this is from the guy who took a week to figure out that C and Assembly files are used together). But I promise to tackle it soon. Thanks.
But Probably won't go this far:
http://www.bathsheba.com/crystalsci/120cell/
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| « Last Edit: Feb 25th, 2005, 9:14pm by st33d » |
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I could murder a pint.
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st33d
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Re: hyperspace transformation
« Reply #5 on: Mar 7th, 2005, 1:29am » |
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Didn't pick through fry's code but watching it made me realise that when you display something in three dimensions on a two dimensional plane, the effect of rotation becomes displacement.
So if I'm drawing a hypercube, all I need to do is draw the real world cube, the hyperspace cube and the lines connecting the corners on the two cubes. Rather than worry about how to visualise the rotation, all I have to do is displace the two cubes to a maximum equal to the cube's dimensions.
http://www.st33d.net/processing/liteDark17.html
Have I got this right?
update: Ah yes I have got it right. I just can't figure out how to spin the hyperspace cube and the real cube on its own axis for the last bit rotation (I'll leave scaling one cube inside the other for another day).
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| « Last Edit: Mar 8th, 2005, 6:25pm by st33d » |
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I could murder a pint.
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