projector

Discuss interdimensional programming, Java applets and so forth.

projector

Postby papernuke » Mon Oct 02, 2006 3:56 am

are there any free projectors on the computer that show pictures of higher dimensional figures and you can move them around?
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Postby pat » Mon Oct 02, 2006 4:29 pm

There are quite a few. What exactly are you looking for?

Do you want slices or projections? Do you want any specific shapes?

As far as mine go, there are:
http://www.nklein.com/products/hsr/
and
http://www.nklein.com/products/crot/

Both of those let you spin the shape around. To drag around the pics in the second one, you probably want to stop the animation.

and soon there will be a more generalized one.

Adanaxis(?) has a hypercube demo, but I can't recall if you can manually rotate it.
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Postby Keiji » Mon Oct 02, 2006 6:19 pm

I'm not too sure about how your projections work, but assuming a projection of 3D down to 2D (like in a 3D computer program) worked like this:

(x,y,z) -> (x,y)z = (xz,wz)

then a projection of 4D to 2D would do this:

(x,y,z,w) -> (x,y,z)w = (xw,yw,zw) -> (xw,yw)zw = (xwzw,ywzw) = (xzw<sup>2</sup>,yzw<sup>2</sup>)

Wouldn't this be better:

(x,y,z,w) -> (x,y)(z,w) = (xzw,yzw)

?

If possible, please implement this in a Java applet so I can see the result.
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Postby pat » Mon Oct 02, 2006 7:27 pm

A perspective projection from 3D to 2D typically goes like this:
* (x,y,z) -> (x,y)/(a+z) = (x/(a+z), y/(a+z))

Doing this same thing from 4D down to 2D in two steps would be:
* (x,y,z,w) -> (x,y,z)/(a + w) -> (x,y)/( (a+w)(b+z) )

For my crot applet, IIRC, I did this instead:
* (x,y,z,w) -> (x,y,z)/(a + bw) -> (x,y)/( (a+bw)(c+z) )

I have, in the past, done this:
* (x,y,z,w) -> (x,y)/(a + bw + z)

The b is there so just so that (0,0,1,0) and (0,0,0,1) don't project to the same place.

In my new applet, I'm going to be allowing much more flexibility in the projection. But, I can't promise that applet this week.
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Postby houserichichi » Tue Oct 03, 2006 2:38 am

You you just make these applets for fun or is it for work/school? At any rate count me as one who appreciates the work and effort!
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Postby pat » Tue Oct 03, 2006 2:44 am

For fun.

In some cases, they help me to solidify things in my mind.

But, the biggest thing for me is that, when I weigh the possible usefulness to people vs. the amount of time it takes me to put one together, there's no question.

The more general one that I'm working on now is going to take a fair bit more time, but it should be lots more useful, too.
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Postby batmanmg » Tue Oct 03, 2006 2:49 am

i second and third that... shank you vewy vewy mush...

anyone know which one is the best for tesseract veiwing?
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