Triply Periodic Meshing for Triply Periodic Minimal Surfaces

pip install -r requirements.txt

• numpy – for numerical operations
• libigl – for mesh cleaning and processing
• meshio – for reading and writing meshes
• pygalmesh – for mesh generation
• polyscope – for visualization
• PyMCubes – for surface mesh generation

NOTE: We use a custom fork of pygalmesh (zfergus/pygalmesh). Install it with:

pip install git+https://github.com/zfergus/pygalmesh.git

rather than pip install pygalmesh.

We use a C++ backend to accelerate implicit function evaluations. To build it, you need to have a C++ compiler and CMake installed. Then run:

pip install -e .

This uses nanobind to create a _tpms module that provides the C++ functionality for evaluating TPMS implicit functions.

NOTE: The _tpms module is included in the TPMeSh package, so you don't need to import it separately.

This will also install the Python package TPMeSh and provides a command-line interface for generating TPMS meshes of the same name.

$ TPMeSh -h
usage: mesh_tpms.py [-h] [-x X X X X X X X X] [-i I] [-s] [-p] [-o OUTPUT] [-t THICKNESS]
                    [-n ELEMENTS_IN_THICKNESS] [-r REPEATS REPEATS REPEATS] [-v]
Generate a TPMS mesh with given design parameters.
options:
  -h, --help            show this help message and exit
  -x X X X X X X X X    design parameters
  -i I                  Generate a canonical TPMS with the given index
  -s, --surface         generate surface mesh
  -p, --periodic        generate periodic mesh
  -o, --output OUTPUT   output mesh name (.stl for surface mesh, .msh for volume mesh)
  -t, --thickness THICKNESS thickness of the TPMS mesh walls (default: 0.5)
  -n, --elements-in-thickness ELEMENTS_IN_THICKNESS
                        Number of elements in the thickness of the mesh (default: 2)
  -r, --repeats REPEATS REPEATS REPEATS
                        Number of repeats in each direction (default: 4 2 4 for full mesh,
                        1 1 1 for periodic mesh)
  -v, --visualize       visualize the mesh

To generate a mesh for a specific TPMS primitive, use the -i option with an integer index.

TPMeSh -i <primitive_index>

where <primitive_index> is an integer from 0 to 7, corresponding to the following TPMS primitives:

(0) Schoen Gyroid	(1) Schwarz Diamond	(2) Schwarz Primitive	(3) Schoen IWP
(4) Neovius	(5) Fischer Koch S	(6) Schoen FRD	(7) PMY

TPMeSh -i 2 -r 2 2 2 -o "2.msh"

TPMeSh -i 2 -r 2 2 2 -s -o "2.stl"

TPMeSh -i 2 -r 1 1 1 -p -o "2p.msh"

To interpolate TPMS shapes, you can use the -x option with the design parameters. For example:

TPMeSh -x 0.4 0 0.6 0 0 0 0 0 -o "interpolation_a.msh"
TPMeSh -x 0 0 0.24 0.2 0 0 0 0.56 -o "interpolation_b.msh"
TPMeSh -x 0 0 0 0.4 0 0 0.4 0.2 -o "interpolation_c.msh"

This project is licensed under the GPL v3.0 License - see the LICENSE file for details. This is in compliance with the original CGAL/pygalmesh licenses, which are also GPL v3.0.