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# Posts tagged with '3D printing'

## Voxel Volumes

One of the main feature additions of the latests version of Functy has been the ability to export as SVX files. Functy could already export in PLY and STL, but both of these are triangle based. They represent the 3D functions as surfaces defined by carefully aligned triangle meshes. Rendering objects using a graphics card also uses the same triangulation process, so exporting as PLY or STL is a very natural extension of the existing rendering.

The SVX format is different though. It stores the models as a voxel image (a voxel being a three dimensional pixel, for those who didn’t grow up through the 90s demo scene). As a result, SVX doesn’t just store the surface, but also the volume of a function.

Turning a triangulated surface into a voxelated volume isn’t necessarily straightforward, but Functy has the advantage of having all its objects originate as purely mathematical forms. In theory, this means voxel rendering them as volumes should be quite easily.

What I found in practice is that for Cartesian functions and spherical functions this is true: they can be turned into voxel volumes in a very natural way. Curve functions are a different story though. In the next few posts I’ll go through each of the processes separately, to give an idea about how the solutions for each of the three function types were coded.

- Intro (this post)
- Cartesian Functions
- Spherical Functions
- Curve functions

## Lissajous Loops

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 Functy rings

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.

## Interactive Functy function viewing

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!

## Functions in the real world

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!