Gyroid 3D Plot

Note: to clone this repo, you need git lfs, because generated STL files, which are big, have been committed.

The Gyroid

The Gyroid has become quite famous in the 3D printing community, for being often used as infill pattern.

To define a Gyroid:

• Take this ℝ³ → ℝ function: f(x, y, z) = cos(x) sin(y) + cos(y) sin(z) + cos(z) sin(x),
• the Gyroid is the surface where f(x, y, z) = 0.

3d Surfaces - skimage and matplotlib

Such kind of ℝ³ → ℝ surfaces can be hard or impossible to express as convenient and iterable parametric ℝ² → ℝ³ functions in the form x = f_x(u, v), y = f_y(u, v), z = f_z(u, v).

• So we are using a Python solver: vertices, faces, ... = skimage.measure.marching_cubes().

• The surface can be visualized by matplotlib.pyplot.show() as done in:

  ./gyroid.py -p  # compute surface and view it
  

  

  Visual inspection is not particularly smooth unless you have a very fast computer, so you're better off generating a volume and inspecting its STL export. See below.

Turning a 3d Surface Into a Volume - meshlib and meshlab

In order to 3D print the surface, we have to give it a volume by adding some thickness.

• To this end, we're using meshlib.mrmeshpy.offsetMesh(offset=thickness).

  • Meshlib is free for education and evaluation.

  • As meshlib and skimage use incompatible formats, we're saving the surface computed by the former to a temporary STL file, read by the latter.

• We apply all the above and save the result as an STL file:

  ./gyroid.py -s
  

  and can view the result using e.g. meshlab.

  meshlab outputs/stl/gyroid.stl
  

  

3D Printing

You can use Cura or any other slicer.

• Follow this link to see a video of the successive layers.
  

Installation and Usage

How to Install

1. Make sure you have Python 3 installed.

2. Install the make commande. Example with Debian-based distros:

   sudo apt install make
   

   Other optional programs are meshlab and cura (or any other slicer).

3. For any OS having Python3, do:

   make venv
   . .venv/bin/activate
   make require
   

How to Run

. .venv/bin/activate
./gyroid.py     # show options
./gyroid.py -p  # show surface in matplotlib; rotation/zoom net performant
./gyroid.py -s  # compute .stl file with thickness (saved to outputs/stl/)

Other Included Surfaces

The surfaces provided in this repo are:

Program	Description	Screenshot	STL
./gyroid.py	The surface described above		gyroid.stl
./lamella.py	A surface accidentally created		lamella.stl
./multiple.py	A collection of surfaces		schwarz_p.stl
./organite.py	An organic section		organite.stl
./scherk-singly.py	A Scherk surface		scherk-singly.stl
All pre-generated STL files			outputs/stl/