help the imagination

Discuss interdimensional programming, Java applets and so forth.

help the imagination

Postby batmanmg » Wed Sep 20, 2006 8:57 pm

does anyone know of, or can anyone make,

something that alows users to rotate many of the 4d shapes, 3 dimensionaly and 4 dimensionaly. I've only ever found one that lets you do this with a hypercube. but it was a very confusing interface. this would be greatly appreciated for vidualizing the more complexe and ill explained shapes. Im sure others will agree.
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Postby Keiji » Wed Sep 20, 2006 9:02 pm

No, but if you're extremely patient, then wait for Fusion's HNET editor. Which will let you do anything in any dimensional shape.
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Postby batmanmg » Wed Sep 20, 2006 9:09 pm

how patient is extremely patient? waits patiently for the answer.
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Postby Keiji » Wed Sep 20, 2006 9:10 pm

Extremely patient is a year or two. :lol:
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Postby pat » Wed Sep 20, 2006 10:16 pm

Here's an applet that let's you rotate a simplex, a cube, or a 16-cell.
http://www.nklein.com/products/hsr/
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Postby batmanmg » Wed Sep 20, 2006 11:02 pm

i wanted it more for more complexe things. but thats useful to those who haven't gotten familiar with those
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Postby pat » Thu Sep 21, 2006 9:43 am

And, here's an applet that let's you set the rotation speed on a variety of simple object.
http://www.nklein.com/products/crot/

I'm not sure what sort of complex things you were looking for....

I'm thinking of adding a way to put in an arbitrary set of points and edges. Would that be useful to you?
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Postby thigle » Thu Sep 21, 2006 7:12 pm

i would definitely be useful for me ;)
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Postby batmanmg » Fri Sep 22, 2006 5:46 am

i was talking about any of the many rotopes that we have a 3d projection for. duocylinder, spherinder, do we have a glome projection?, cubinder, duoprisms, and the biggest reason for this is prismic cylinders
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Postby pat » Fri Sep 22, 2006 5:18 pm

I have a mesh version of a glome in there now. I can add in cubinder and spherinder easily enough and should be able to add in duocylinder.
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Postby pat » Fri Sep 22, 2006 6:22 pm

Okay, I added cubinder, spherinder, duocylinder, tiger, toraspherinder, toracubinder, torinder, tetratorus, and 4-octahedron (16-cell). If you point me toward references for duoprisms and prismic cylinders, I'll see what I can do. (Parametric versions would be the best.)
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Postby thigle » Sat Sep 23, 2006 1:20 pm

very nice.

what would make it even better than it is perfect right now, is one of these implementations for even further clarity of pointing to the actual 4dim objects:

1. color coding for 4th coordinate of the object
2. line-width variation for perspectival truthfulness
3. apparent intersection of edges

ad1: what would also be very nice and instructive is a color coding for depth, similar to this 24-cell animation. (from Tony Smith's webpage)
Image
or this hypercube one.
Image

they both use color to code the 4the parameter of the realmic shadow.

should you be implementing it into your viewer, please use the natural gradient of the spectrum of light as it refracts through a prism, or as you can see in a dewdrop or rainbow, as that is the best and most healthy gradient to psyche, it fills the whole spectrum.

ad2: things in perspective seem to shrink in size with increasing distance. applying this on a micro-scale to the edges of projections, you could make the closest points let's say 5 pixels-wide, while the most distant can be 1pixel-wide.

this can be seen in Hilbert&Cohn-Vossen's Geometry & Imagination, where the hand drwan pictures all share this property of lines diminishing in their thickness as they go further from the viewver.

ad3: this is a graphic technique which is mostly used in hand-made graphics, like woodcuts etc: when working in monochromatic expression mode, the artist must often create an impression of depth between 2 lines or thin objects (wire, rope,...) that cross. to this effect, the pixels of the line which is deeper in the picture plane and which therefore runs behind the other line/edge, at the points where it 'touches' the closer line/edge, these pixels are omitted.

so if the background is black, and the lines are white, the line/edge that is closer to perceiver has 1 black pixel on each sides of it in such a way that the last pixel of the line/edge that is deeper before it crosses the closer line from any side is ommited.

any of these might be possible ? the color coding might be easy as you just use the 4th parameter to attribute a color-value from defined color-range.

as for the second, it might be harder, depends on the resolution also.

i would prefer if your viewer could be also toggled into bigger resolution, it's a bit tinyish.

anyway, great work, undisputably the best 4d-objects viewer ever.

p.s.: 4. one more thing which would be perfect and ground breaking, would be if you implemented what sullivan has in his stereoscopic projection applet: http://torus.math.uiuc.edu/jms/java/stereop/

the two sliders to the right are great, but i would be mostly interested in how does it look like for certain objects you have in your list when seen in stereoscopic projection (stereoscopic is like mapping between rieman's sphere and complex plane, one-to-one. is there such a mapping between Q and some 3space(object) ? what shape does the quaternionic algebra map onto in one-to one fashion, similarily as the complex plane maps onto sphere ?
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Postby batmanmg » Tue Sep 26, 2006 4:33 am

when you look at the glome and other smooth 4d shapes, how are you able to distinguish the mesh from the shape? the 3d sphere was easy enough, but there wheren't a bunch of them overlaping. maybe if there was a 3d slice highlighted that might help. i know getting smooth models is near impossible, but maybe one day some higher learning center will come out with one.
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Postby thigle » Tue Sep 26, 2006 10:21 am

there is an animation of sliced smooth glome somewhere at pat's website, with color coding.

it is quite tiny and fast for me though.

hey pat, what about those 4 proposals for upgrade of your viewer ? you see implementing any of those as real in the next few years ? :D
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Postby pat » Tue Sep 26, 2006 7:14 pm

thigle wrote:1. color coding for 4th coordinate of the object
2. line-width variation for perspectival truthfulness
3. apparent intersection of edges
4. stereoscopic projection


Right now, I'm using the java.awt.Graphics.drawLine( x1, y1, x2, y2 ) method to draw lines. I'd have to replace this for #1. That's possible, but annoying.

Of course, I'll have to replace it for #4, too.

For #4, you're just wanting to see more shapes and stereo-pairs of stereographic projections? That should be easy enough.

Let's move this over to this thread:
Towards A More General 4D Object Viewer
I'll start a list of desired features there.
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