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.
I finally managed to get the video to record properly, so here’s a video version of the shader-based depth-of-field focus-blur.
P.S. This post was actually made using Ubuntu phone. The browser’s still a bit “experimental” so it’s been a bit tricky, but it does seem to work!
One of the difficulties with 3D visualisations - and network visualisations seem to suffer especially badly from this - is that while they’re a great way to represent complex data, they rely on animation for much of their clarity. This stems from the fact that the third dimension is illusory. The fact is we’re still largely stuck with 2D screens that our 3D images get projected onto. Until we move to proper volumetric displays, even the current attempts at 3D (stereoscopic) displays won’t fix this.
For the moment then, the best way for us to understand the lost depth component is by shifting our perspective, or in other words, by moving things around.
However, there are other ways to approach this and in the past I’ve been incredibly impressed by the way blur can be used to improve the perception of depth. This can give a really nice effect of camera focus, where different parts of the image have different levels of blur applied depending on whether they’re in or out of focus.
Testing this on some of the network graphs that I’m currently working with has produced some really quite nice effects. Ironically, by making parts of the image less clear, the overall coherence and clarity of the image is improved substantially. Here are a couple of screenshots of a random network with focus blur applied, both from up close and from a further distance.
The effect is achieved by rendering the whole image to a texture framebuffer. A very simple fullscreen shader is then applied, which increases or decreases the level of blur for a given pixel depending on the z-buffer depth value at that point. It’s a really very simple technique, but in my opinion produces some quite effective result.
This is one of the reasons why shaders are so phenomenally powerful. The depth blur is a very short program, but it needs to be executed for every single pixel of the image. That’s a lot of pixels, and a lot of computing power is needed to do this. Applying a shader program in parallel across the whole image is hugely more efficient than getting the CPU to do it. This allows it to be applied in realtime for each rendered frame, without stretching resources, even on my relatively underpowered laptop.
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.
After prompting by Tony’s superb gallery of images, I’ve spent a bit of time playing around using Blender to render models created using Functy.
This has also prompted a bit of extra functionality, and I’m hoping it will soon be able to export out multiple models from Functy to support animated functions. Using the current experimental code (there’s no front-end yet, but it’s in the pipeline) I managed to generate a kind of animated mercury whirlpool. It’s up on deviantart, and if you’re happy to wait for the download, please do take a look at the full animated version.
Tony Ralano has been creating some amazing renders by combining Functy models with his impressive Blender and 3DS Max skills. The image below is an example of a function exported out, then manipulated and rendered using Blender.