Tag: 3d

A Simple and Elegant Cloaking Device

By Anupum Pant

In the year 2011, UTD NanoTech unveiled their carbon nanotube invisibility cloak, making us move one more step closer to realizing a piece of magical cloth which fictional characters often use to turn themselves invisible. And then there was a 3D printed invisibility cloak too.

A few researchers at the University of Rochester have now created their own elegant version of an invisibility cloak. It’s, in principle, a fairly simple optical device which uses just four lenses to cloak objects behind it, keeping the image behind it still visible.

In fact, whatever it does, it does it in 3 dimensions. That means, the viewer looking through the device can actually pan to change the viewing angle and can still see the image of the background, undistorted, as if there were no lenses in between, in real-time. And it is probably the first ever cloaking device to be able to do that.

The device has a blind spot (sort of). In a way that It doesn’t cloak anything that lies in the axis of the lens system. The cloaking area is in the shape of a dough nut. Any part of the object that accidentally enters the axis area becomes visible and conceals the background. The device is simple and cheap enough to be easily scaled to cover greater area, as long as lenses of that size can be made. The video explains it better.

via [Quarks to Quasars]

[Video] Stunning Animation of How HIV Works

By Anupum Pant

Sorry, it was the FIFA WC finals, my favourite team (Germany) won, and I was too excited to write a lot today. So I searched my notes for something interesting to share quickly.

I found this 3D medical animation that I had bookmarked a long time from now. It is an animation of how the HIV replicates. It’s one of those videos with a lot of jargon where not everyone would understand what’s really happening, unless they are a lot into biology. If you are not, then I’d suggest muting the sound (don’t actually) and just watching the biological machines at work.

Still, it is amazing to see how things work at a very very tiny level and it’s an immense pleasure to appreciate how little biological machines work around in bodies to accomplish so much.

Moreover, it makes me very happy that we’ve come so far in science to understand so many things that we are now able to make mesmerizing animations of the extremely complicated and seemingly abstract biological mechanisms.

Script, Storyboard, Art Direction by: Frank Schauder, MD
Animation: MACKEVISION
Publicity: Dr.Rufus Rajadurai.MD. | D.DiaDENS

Constant Width Objects – Not Spheres!

By Anupum Pant

Until today, I had no idea that non-spherical objects could have the same diameter at every point! Don’t believe me? Have a look at these wonderful little metal objects that aren’t anything even close to a sphere and are still able to roll a flat surface on them, as spheres would. [Video]

Like Gombocs, these shapes are a Mathematician’s fantasy. They have a generic name – constant width objects. In fact, these carefully machined metal objects could be perfect gifts for your mathematician friend. I know, I would some day, if you think you need these too, you can buy them here. (I’m in no way related to Grad-Illusions, nor am I an affiliate marketer)

Note: Though in some manner they look like Gombocs, they are not Gombocs. To know more about what Gombocs are, read this – [Gomboc – An Object That Never Falls]

How are they made?

Theoretically, to understand how they are made, you need to understand that the 3D objects of constant width are usually* spun out of a 2D object – Just like a sphere can be made by spinning  a circle. Though there is a kind of constant width 3D object that is not a spun version of any 2D curve.

50 Pence coin 1994 - 50th anniversary of D-Day...
50 Pence coin 1994 – 50th anniversary of D-Day – Normandy Landings (Photo credit: ell brown)

The 2D form is called the Reuleaux triangle and it looks like this [image]. The one shown in the link is a constant width curve based on an equilateral triangle (triangle with equal sides). It turns out, you can construct a constant width curve out of any triangle, and a polygon too (like the 50 pence coin shown above made out of a regular heptagon). To make a constant width curve using an equilateral triangle, all you need is a compass, a paper and a pencil:

  • Draw an equilateral triangle.
  • Put the point of your compass on one vertex.
  • Trace out an arc that starts from one of the other vertex and ends at the third one.
  • Repeat the same for rest of the two vertices. There! You have your constant width curve. Cut it out of paper.
  • Now around an axis dividing the shape into half, spin it. You have a theoretical 3D shape that resembles the one shown in the video above.

Vehicle tyres and square hole drills

So, since these shapes can roll things around like circles can, wheels could be made of these shapes too! Then, why aren’t wheels made that way? That is because when these shapes roll, they don’t have their centers at one place. If vehicles had tyres like these, engineers would have had a hard time designing axle systems.

They are in fact used in a Wankel engine. And since the center traces a square when Reuleaux triangle rolls, they have been used in drills that can drill out square holes.

Random constant width facts:

    • There are a few pencils which are manufactured in an extruded-reuleaux triangle shape. These pencils can roll around smoothly like circular pencils.
    • For some reason, even guitar picks are often manufactured in these shapes.
    • Instead of spinning around a constant width 2D object, a 3D constant width object can be made by modifying flat tetrahedron faces using intersections of sphere faces. As it can’t be done on a lathe, these are particularly hard to machine. It is called the Meissner’s tetrahedron or the Reuleaux Tetrahedron.
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Klein Bottle – A Bottle That Contains Itself

By Anupum Pant

To appreciate the beauty of mathematics and nature there is no escaping without learning about a Klein Bottle. A three-dimensional representation of a Klein bottle looks like this – [image]

There are number of phrases you can use to describe (not exhaustively) it. A few of them are as follows:

  • An object with no boundaries.
  • An object with no inside or outside.
  • One sided surface.
  • Non-orientable surface

Wikipedia describes it as:

The Klein bottle is a non-orientable surface; informally, it is a surface in which notions of left and right cannot be consistently defined.

Simplifying things: A Möbius strip is a simpler example of a non-orientable object. That means it has no inside or outside. Add another aspect – having no boundaries – to it, it gets more complex and you end up with a Klein bottle.
If you haven’t heard of Möbius strips, to understand such surfaces, you can make one for yourself now.

  1. Tear off a strip of paper.
  2. Hold it horizontally, straight with both of the short edges in your hands.
  3. Now, twist one of the edges by 180 degrees and join the two short edges. You’ll have something like this in your hands – [image]

Test the surface and edges: On this object you just created, move your finger along the surface. You’ll find that your finger comes  back to the same place eventually. There is no inside or outside for this object, there is just one surface.
The same thing happens with its edge (try moving your finger along the edge). Here is a Music box playing a Harry Potter theme continuous – forward, inverted, forward and so on – manner; Relevant video: [video]

Now spin it (the Möbius Strip) fast. You can NOT practically do it. I mean, spinning it like you spin a circle and get a sphere. There! You have a Klein bottle. It is better than a Möbius strip in a way that it (Klein Bottle) has no boundaries.

Klein bottles cannot actually exist in our three-dimensional worlds, the ones that look like them (Klein Bottles) are just 3D representations of a 4D object. Like a two-dimensional drawing of a 3D cube. These models are available for you to buy. Interestingly, in spite of having no inside or outside, they can be filled with a liquid. But, given the opposing force of air, they are pretty tough to fill. It is important to note that the 3D representation of a 4D Klein bottle has an intersection of material, this doesn’t happen in 4D. It is like the intersecting edges of a 3D cube in the 2D representation.

You’re thinking 3D? At MIT (and other places) 4D printing is already happening.

If you are having a tough time imagining this 4D object, the following 4D animation might help (or leave you perplexed) – [video]
[Extra reading for math geeks] as if they already didn’t know about Klein bottles.