2012: The Beginning of the End for Polygons
Aaron Trocola posted on July 17, 2012 | | 8609 views

MandelbulbPolygonal models, and especially the STL format, have been the standard way of describing objects for additive manufacturing as long as the process has existed. The field of computer graphics adopted polygons mostly out of necessity, since the memory and computing power requirements of other methods have been impractical until recently.

Now, I believe we are finally ready to see polygons take a backseat to 3D alternatives. And having worked with 3D models for over 15 years, I would be very happy if I never had to click on another triangle ever again.

With the adoption of volumetric representations —models that are not just a 2D surface in 3D space — we will have more efficient definitions and greater control while unlocking a unique asset of many additive technologies.

What are the alternatives?

The two main volumetric representations of 3D models include the solid modeling formats used in CAD and voxels, the 3D analog of image pixels.

Solid models have clear advantages in that they have a mathematically constrained inside and outside. The high degree of precision in modern manufacturing would be impossible without solids, yet they are still lacking in the context of additive manufacturing. 

The very intricate lattice structures often used in AM parts have so much surface area that the memory footprint of a polygonal representation exceeds the voxel one by many times. Solids (b-rep) are even "heavier" than polygons, and while they are more accurate, the amount of processing power needed to calculate an object with many thousands of discrete features makes solids impractical for many AM applications.

That leaves the voxel-based volume representation, which can be thought of as a stack of 2D pixel-based images. Rather than a simple binary inside and outside, voxels can have spatially varying properties, such as partial densities, different materials, color and other characteristics embedded into its 3D space.

For reference, I have written an extensive blog post detailing an example that compares voxel and polygon representations with links to the data.

How can we make use of volumetric data?

There are recent developments in volumetric data for 3D printing that we are hopefully about to see come to fruition. These developments are mostly limited to software. There is still no standard way of implementing low-level addressing to 3D printers, though Neri Oxman was able to work with Objet to use volumetric printing to produce her presentation at Pompidou. Multi-material designs with that level of complexity could not be represented in a practical way using polygons.

What has changed recently is that people are finally catching on to the strengths of voxel-based representations. I had a great conversation with Alexander Oster, the CEO of netfabb, at the RAPID 2012 conference about using volumetric data in additive manufacturing. Netfabb Studio uses Selective Space Structures (3S) to generate open lattices throughout the volume of a model. I immediately recognized that netfabb is creating and storing a volumetric representation of the model. It does so by voxelizing the model and placing a mesh lattice unit at each location, a big step toward true volumetric printing.

My simple request was to import a volume as a sequence of images and be able to output this structure directly as slices, bypassing the familiar polygon representation (STL). I sent Alexander some data samples that, along with many others, I am making available through the Thingiverse website. I won’t speculate as to whether or how my request influenced change, but coincidentally this recent thread on the Ultimaker forum hints that volumetric printing will soon be possible and publicly accessible on at least one type of 3D printer. [Edit: NetFabb's "Volumetric Printing" in version 4.9.2 refers to a filament feed-rate control method. Image sequence import has not yet been implemented in this release.]
Unfortunately, the volumetric pipeline will remain incomplete until voxel-based printer manufacturers change their hardware to accept that kind of input.

How can this be adopted?

Unfortunately, the popular fused filament fabrication (FFF) used by the Ultimaker — and the Fused Deposition Modeling (FDM) method from Stratasys —  is not a very appropriate process to capitalize on volume printing. Other more costly processes like SLA, laser sintering and EBM could be considered voxel based, but only the Z Corp (now owned by 3D systems) and Objet machines are capable of multi-channel output.

Still, it is possible to derive great advantage from volume representation in the context of FDM/FFF, and even some CNC machining, by converting solid models directly to a more flexible voxel format and generating tool-paths from those, avoiding the use of polygons.

Yet, until formats and hardware evolve to support volumetric input, we will have to limp along, converting our volumes to massive polygon data sets. However, we can leverage earlier work, such as the polygonization issue addressed by William Lorensen and Harvey Cline in the 1980s. They created the Marching Cubes algorithm to make meshes from CT/MRI data. The patent has since run out, and the source code is freely available for adaptation to additive manufacturing.

Will the DIY scene get there first?

The glacial pace of hardware development and standards adoption in industry means we may see this type of data pipeline evolve in the 3D printing hobbyist community before large companies can position themselves to address the problem. As I stated, the most common 3D printers are not using ideal processes for voxels, but it is definitely worth implementing so that the concepts can be tested and the software refined. This way, it will be ready when the hardware is adapted to the new standards.

Creating a hardware/software manufacturing ecosystem is a difficult challenge with many inter-dependent issues. It's a chicken-and-egg problem, but we have to start somewhere, and the more minds that are put to it, the sooner it will be resolved. Since not everyone can develop hardware, one good strategy is crowd-sourcing a software environment and establishing standardized hybrid data structures.

Eventually the system will become so mature and the utility so glaringly obvious that the hardware makers support it or risk being left behind by people working in their garages.

Implications for professional CAD

The next step for developing this technology for use in industry is to adopt the hybrid solid/voxel format and build tools for the creation of this type of model in CAD. This is essential for making use of technologies like Objet's multi-material printing. Right now, each variation of material must be stored as a separate STL file, which makes advanced applications difficult or impossible.

If designers could easily define material properties throughout an object, the possibilities for design using AM processes explodes into a variety of forms that are far outside what is normally considered in modern part design. There are some software packages that convert to and from different data representations, but none of them have what could be described as volumetric material design and editing capability. Two systems that have a lot of potential are Sensable’s FreeForm and Uformia’s Symvol plug-in for Rhino. They use both surface and volume representations, albeit with one material and no integrated format for output since one does not yet exist.

One potential development pathway for creating a system that treats models as entities with a solid/voxel duality involves adaptation of new simulation algorithms. These systems use what is known as the Immersed Boundary Method (IBM), which has many advantages over the traditional Finite Element Analysis (FEA). IBM can solve a simulation without having to generate a 3D mesh of the part, an often complicated and problematic step. Much like the wave and particle duality of quantum physics, the part exists in both domains simultaneously by having the continuous surface of the solid embedded within a discrete Computational Fluid Dynamics (CFD) grid of the sort normally used for gas and fluid flow simulation. The clear advantage this has for simulation also applies to the modeling and production stages of a design. This unified approach will be the future of additive manufacturing and manufacturing in general.