The goal of this project is to provide more effective mechanisms for error detection of 3D printer failures through the use of ‘structure for motion’, computer vision and computational geometry. Furthermore, first steps in order to achieve this goal is to determine what actual constitutes an error and what types of errors the application will focus on (if not all).
So what next??? We need to make some “error free” prints in addition to “intentional error” prints in order to establish a base line for tolerance and to compare the two. Also, creating a workflow for reconstructing 3D models from 2D images is coming and this is where structure for motion comes in handy.
Of course, further exploration of literature on the subject will be continuing.
This past week I have read over the official OpenSCAD documentation and achieved a limited but sufficient understanding of the OpenSCAD scripting language.
To the Sphere Packing software, I have added a new file output for the graph edges as well as a file output for the mesh triangles.
Unfortunately, since it doesn’t seem like OpenSCAD has a direct way of pulling input from general files aside from standard 3D object files such as STL, OFF, and AMF, I have to manually copy and paste the file outputs from Sphere Packing into an OpenSCAD file. On the bright side, I have made the file outputs to be vectors of points that are already in scad format so copying and pasting is all that really needs to be done. I have written a simple scad script file that takes the graph data and mesh data and generates corresponding solids.
Here is a picture of an example solid for a graph from Sphere Packing:
The solid above took several minutes to render since the level of detail is relatively high. Next, I constructed a hollow shell from the triangles of the original mesh to fuse with the internal graph structure as a cover. The results are demonstrated below:
These solids are all union-ed together to create one solid which is then exported as an STL file. The object can be sliced with any 3D slicer program and then printed using existing 3D printers.
Hopefully, I’ll get to print a physical model this week.
Thanks for reading,
A major goal of my Sphere Packing research is to actualize the mathematics and computer models into novel techniques for the mesh generation portion of the 3D printing process. To this end, we need a way to complete the full process starting from an STL model of a 3D object and ending with a 3D printed object. With the current software, we have already established a way to generate the meshes; however, we do not yet have a way to print the meshes. As partially mentioned in the previous post, we came up with two possible approaches for printing the meshes. The first method that we will try involves the conversion of a mesh into a solid using OpenSCAD.
A simple illustration of this idea is shown below:
Having the solid, we could then use traditional slicer software to generate the G-code for printing the object.
Also, we can use OpenSCAD’s shape union and intersection functionalities to combine the shell of the original object with the internal infill mesh to create a print object that would have the shape of the original object but with a semi-hollow internal support structure consisting of the mesh from sphere packing.
The general idea is produce a lightweight solid with a strong internal structure that can withstand great stress. An analogy to a natural structure with this quality would be bird bones which are necessarily lightweight for flight yet they can withstand the constant pressures from flight motions.
The specific implementation of this procedure is in progress, so stay tuned. ~
Thanks for reading!
Since the last time I posted, I have added the ability to generate a different lattice structure to the Sphere Packing software. This new lattice structure is called the hexagonal close packed (hcp) lattice. It is one of the tightest ways to pack equally sized spheres, with the other way being the face-centered cubic (fcc) lattice which only differs in the way that consecutive layers are aligned.
In the above image, a bird’s-eye view of hcp packing (left) and fcc packing (right) is shown. The underlying hexagonal arrangement of white spheres representing layer 1 resembles the tightest way of packing equally sized circles in a plane also known as a penny-packing. Every layer of the hcp and fcc lattices has this identical hexagonal arrangement. The black spheres representing layer 2 are placed over the gaps created between three underlying spheres. Note that layer 2 and layer 3 are not fully drawn out so that the lower layers are not obscured completely. Also note that layer 2 is identical for both hcp and fcc lattices. The difference is from layer 3 which lines up with layer 1 in the hcp lattice, but is shifted in the fcc lattice.
Anyways, back to the main point. Hexagonal close-packed lattices are now available to use in the sphere packing software. Earlier there was only body centered cubic lattices:
Now here are the hcp lattices:
With this new type of lattice we hope to gain insights into how a different set of combinatorics affects sphere packing.
Moving forward, I would like to 3D print the meshes generated by the sphere packing. The difficulty lies in the fact that the meshes are not solids, so traditional 3D slicer programs can not work with the mesh output directly. Thus, one approach would be to convert the mesh into a solid. As it has been suggested to me, this could possibly be done using OpenSCAD. Another approach would be to skip the slicer step completely and directly generate gcode from the mesh using a toolpath planning algorithm. I will first try the method of converting the mesh into a solid since it seems easier than developing a new algorithm for toolpath planning in 3D space. I will keep you posted on the results.
Thanks for reading!
I wish to propose a new method of generating new infill meshes for 3D printing objects. However, let me first give a brief background. Over the summer I worked as a software developer at Oak Ridge to create a suite of tools that apply the mathematical concepts of Circle Packing to generate graphs (Computer Science graphs) that were later used as the meshes for infills. The overall goal was to create meshes that used less printing material but had sufficient physical integrity to still perform its role as a support structure. The end result would ideally be a strong mesh that was still light-weight. An image that illustrates this is shown below:
I will also add here that we wanted a way to “densify” the mesh in custom regions in order to selectively increase the physical strength in specific areas of the print. In the image above for one layer of a 3D airplane wing, based on the assumption that the edges would experience more stress, we selectively refined the mesh in 2 layers around the edge using a technique developed by Ken Stephenson, a math professor at the University of Tennessee.
Later on, the project leader for this area of research at the Lab, Greg Dreifus, suggested that we could maybe extend the concepts to 3D. Specifically, he wondered if we could build 3D meshes instead of 2D meshes by using Sphere Packing instead of Circle Packing. In order to demonstrate the idea, I worked on a new software that generates a Sphere Packing given a 3D object encoded in an STL file. This new software is based largely on a Circle Packing implementation by John Bowers, a computer science professor at JMU. An example of the software’s capability is shown below:
We hope to further develop the software into a tool that can produce meshes of varying density in custom regions of the 3D object.
Thanks for reading,