July 2013 Archives

Projections

  • Posted on July 30, 2013 at 6:10 pm

The sun was out in Liverpool today, creating crisp and long evening shadows. So it seemed like a great opportunity to take photos of recent 3D printed Functy objects. The full images are rather large, but show the grain of the printing, which I think is rather interesting in itself. Click on the images for the full views.

The original Lissajous is up on deviantArt and Shapeways; the alien egg is also on deviantArt and Shapeways.

Comparing renders with reality

  • Posted on July 27, 2013 at 11:33 pm

Shapeways delivered a new batch of 3D prints recently. I was particularly pleased with the Alien Egg print of a spherical function with the formula:

radius = (3*(0.5+(sin(cos(a)+(p*((3+cos((pi*0.3)-1.5))/4))*10)**2)+((6/6.6)*((2+sin(8*a))/3)**4)))*sin(p)+(4.3*(1-(sin(p)**2))),

colour (R, G, B) = (r/8, (3+sin((a)*8))/5, (3+cos(a*8))/5).

The print is actually rather small (just 6 cm diameter) and the ridges of the shape are really quite delicate. In spite of this, the 3D print has come out really very similar to the original design. I guess you might expect it to be pretty similar, given the way it was produced directly from the model! However, if you look really closely at the original you can see the strata through the object created by the printing process. What I’m really impressed with, though, is the colour produced. I’d expected this to be a bit washed out, but in practice it’s a pretty impressive match.

Below is a comparison of (from top to bottom) the Functy render, the 3D print and a render done using Blender Cycles. In case you’re interested and your browser supports APNGs, there’s also a peculiar animated version!

Alien Egg Comparison (Functy, 3D print, Blender; click to enlarge)

Alien Egg Comparison: Functy, 3D print, Blender (click to enlarge)

Lissajous Looping

  • Posted on July 15, 2013 at 12:40 am

Following on from my previous post, I thought it’d be interesting to make an animated render of the Lissajous figure. If you have an APNG-capable browser (e.g. Firefox) you can see the result on DeviantArt.

While it’s neat to be able to print static versions of these Lissajous figures, in the future I’m sure it’ll be possible to make the fully moving version as well. Now that would be really something!

Static version of the render - click for the animated version

Static Lissajous render - click for the animated version

Lissajous Loops

  • Posted on July 11, 2013 at 8:11 pm

Sines and Cosines have been responsible for some of the most elegant mathematical constructs. Lissajous curves are a particularly simple, yet elegant example. Put simply, a Lissajous is a parametric curve where each axis follows a sinusoidal path. By tweaking the amplitude and cycle length for each axis, a myriad of different patterns can be generated, from circles to intricately woven lattices.

The parametric curves in Functy are particularly suitable for generating nice Lissajous curves, and as usual, they can be output for 3D printing. The results of pumping them through a 3D printer, courtesy of Shapeways, can be seen in the photos below, along with a Blender Cycles render of one of the curves.

If you fancy getting really up-close-and-personal with them, you can order your own copies as unusual desk ornaments, from the Shapeways site.

3D printed Lissajous curves

3D printed Lissajous curves

3D rendered Lissajous curve

Rendered Lissajous curve

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