Experiments in Rapid Prototyping

Written by Paul Bourke
January 2005

The testing here of the ZCorp colour rapid prototyping machine were geared towards determining how far one can push the technology and how useful it might be for mathematical and scientific visualisation. While these particular machines are one of the most advanced and general, they still place some significant constraints on the models they can represent. Perhaps the most serious involves the infusion process after the model has been built, the model can be extra delicate during this infusion process. This places an extra constraint on the thinnest structure over and above what the machine process can create.

The machine in question has a volume of about 200 x 200 x 250 mm. The first tests below were intended to investigate the value of creating solid models of mathematical shapes, in this case supershapes.

  Fractal, Sierpinski sponge

Character from an animated movie (by Russell Scott)

The following model is somewhat more demanding, firstly the wings are very thin, and secondly the model is not free standing so until it is infused with hardener it can't easily support itself. Indeed most damage to the model occurred not by the "printing" process but by the infusion process which removed the structural strength from a number of parts of the model, this seems to occur when the infusing fluid saturates right through the model.


The STL format used to represent the monochrome models here has no support for colour. The software that drives the machine expects VRML descriptions for colour models. VRML models are not difficult to create in code given parametric equations for the surfaces. The quality of the colour, see elliptic torus, was surprisingly good. This model was created intentionally with a continuous colour ramp to test this.

With regard to mathematical visualisation, it is immediately obvious once it is placed on a table that the tetrahedral ellipse is perfectly flat on all sides, something that is not at all obvious from computer based exploration.

Elliptic Torus and Tetrahedral Ellipse

Astronomer by Russell Scott

Building physical models
using the ZCorp Z402 3D Printer

Written by Paul Bourke

See also Borromean rings
and specification of the STL format. October 2000

In 2000 ZCorp introduced a new range of rapid prototyping machines. This was a good opportunity to create a physical object from one (or more) of my favourite 3D models. The model I chose first was the Borromean rings. Many 3D printers for rapid prototyping are based upon liquid polymers and lasers that trace out the contours. These present serious restrictions on the types of models because it is difficult to create models that require self supporting structures during their creation. The ZCorp type of device (and others) use a powder which supports structures as necessary as the model is being built. In addition, a feature not used here, their device can create colour models.

The model chosen is defined by 3 interlocking curves in 3D space. The industry standard format for describing models for stereo-lithography is called the STL format and it only describes solid objects not curves, lines and points. There a number of ways of forming solid pipes, a rather inefficient method was chosen here but one that is easy to create, can be extended to all curve based forms, and reliably represents the curve. The method is simply to "stack" spheres (described as STL format) along the curve. The thickness of the curve can be controlled by using different radii. Depending on how close the spheres are placed the thick curve can be given a smooth, ribbed, or beaded look. A subsequent implementation that is much more efficient and doesn't have the ribbed surface effect is to use cylindrical elements for straight sections of the curve.

The top curve on the right is the one actually used to create the model. The second and third images show a smooth and rougher version.

Source code

The source code that creates the model used in this discussion is given here. It can be readily modified to create any mathematical curve. The most useful part will be the function that creates a sphere in STL and geom format. The geom format is the format used locally to view stereographic images, in this case it was used to test the appearance of the model before sending it off to be created.

And finally here's the finished product. The three links are loose and can be moved around as one would expect. The bone-like fell of the material is not unattractive.

STL format

Representing triangular facets in the STL format is simple, for example below is the first polygon from the model created here. All the polygons are normally encapsulated between "solid" / "endsolid" tags.

facet normal -0.194944 0.980048 -0.0387767
outer loop
   vertex 1 0.37735 -0.333333
   vertex 1.07071 0.392574 -0.304044
   vertex 1.07654 0.392574 -0.333333
The whole model as a compressed STL file: borromean_stl.gz.

Example 2 - Knot

The mathematics behind this object is given here as knot 3.

The model as a compressed STL file: knot3stl.gz.

The source code that creates the model is knot3stl.c.


Other examples (2007)

ASKAP telescope model


Rocks and fossils

Sirovision cliff face models

In the following a terrain (cliff) was recreated, the original surface and texture map is automatically generated by taking two photographs of the cliff face. Software called "Sirvision" can then recreate a 3D mesh surface from the two images, one of the images can additionally be applied as a texture map.

In general successful rapid prototyping require solid objects, not just (infinitely thin) surfaces. This is certainly true for the ZCORP machines, while the model can be structurally strong after curing, it can be quite delicate beforehand. The surface mesh here is simply extruded a fixed distance, this works because the surfaces here don't have "caves".

Top surface


The following are two images of the modelled surface.


400 million year old Placoderm embryo

Calabi-Yau model

Examples from 2012-2014

Photogrammetrically derived bust of Socrates, UWA.


Mine Pit

Earths Oceans


Chain mail