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.
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!
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!
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.
As part of an experimental game project I’ve been trying to use the Functy rendering routines to visualise network structures. At the moment it’s at a very early stage, but has - I think - already generated some interesting results.
The screenshot below shows a network of 60 nodes, each one rendered as a spherical co-ordinate function, joined together using links rendered as curves. I just plucked some simple functions out of the air to see what the results would be like but am hoping to extend it with more interesting shapes as things progress.
The various parts of the network are a little hard to discern with a static image, but when I tried to capture a video the result was a mess of fuzzy artefacts (I think there must be something going wrong with my screen capture software), so I gave up on that.
The next step, after neatening up the code, is to arrange better animation of the nodes and links, with dynamic movement based on things like the forces between the nodes. I’m hoping this will produce some really nice effects, and if anything comes of it I’ll put a bit more effort into getting a successful video capture.
A parcel arrived from Shapeways recently containing some of the 3D printed ring prototypes I generated using Functy. The models were exported directly from Functy and converted into STY format before being directly uploaded to Shapeways for printing. All based on sine/cosine curves, there’s a flat version, a slightly bulging version and an irregular version. Since Shapeways did such a brilliant job printing the prototypes, the next step is to get them to print them in silver. Click on the links if you fancy having your own printed!
The Functy function files for all of these rings are up in the repository and will be included as example files in the next full release.
One of the obvious but neat consequences of having the new STL export functionality from Functy is that the generated models can be imported in to other things. One of these things… well, p3d.in provides a clever HTML5 in-browser model renderer, which means the models can now be rendered interactively directly into this site (or indeed any others). Check out this version of a ball made from string, generated as a couple of curve functions in Functy. Just click and drag to rotate the model. And if you like it, you can even print a copy in 3D!
This afternoon a very exciting (at least for me!) parcel arrived all the way from Eindhoven in the Netherlands. The first ever ‘real’ 3D function generated using Functy and printed by Shapeways using a 3D printer.
I’m really pleased with the results. Shapeways were not only able to print out the rather convoluted function in 3D, but they also printed it in full colour too.
Here’s a screenshot and some photos of the final result.
The colouring is really great - much more vivid than I’d expected - and it’s not as delicate as I’d feared (it survived the journey through the post, at any rate!). This is a spherical function, which is the easiest to print (they generate meshes without holes automatically, which are needed for 3D printing). Hopefully the next step will be to attempt a parametric curve print.
If you want to play around with the model yourself, you can download the Functy definition file, or if you’re feeling flush, order your own 3D printed version from Shapeways. Such is the beauty of 3D printing!