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🔷 Geometry Definitions for Lattice Structures

The unit cell geometries used to generate lattice structures are defined in JSON files, which are stored in the src/geometries/ folder of the project.

📁 Structure of Geometry Files

Each JSON file includes:

  • a name (string)
  • a description (string)
  • a list of beams
  • optionally, a dictionary of parameters

Minimal example:

{
  "name": "BCC",
  "description": "Body-Centered Cubic [BCC] lattice structure",
  "beams": [
    [0.0, 0.0, 0.0, 0.5, 0.5, 0.5],
    [0.5, 0.5, 0.5, 1.0, 1.0, 1.0]
  ]
}

Each beam entry represents a line between two 3D points:

[x1, y1, z1, x2, y2, z2]

⚙️ Parametric Geometries

A geometry file may include a "parameters" block that defines named variables or symbolic expressions:

"parameters": {
  "hgeom": 0.35,
  "angleGeom": 20,
  "valGeom": "hgeom - tan(angleGeom * pi / 180) / 2"
}

These parameter names can then be referenced in the beam list:

[0.5, 0.0, "hgeom", 0.5, 0.0, "1 - hgeom"]

✅ Supported Expressions and Functions

Expressions are evaluated using SymPy, allowing the use of safe mathematical functions only:

  • Trigonometric: sin, cos, tan, asin, acos, atan
  • Exponential/logarithmic: exp, log
  • Other: sqrt, pi

⚠️ Do not use math. in expressions. Just write tan(...), not math.tan(...).

🔁 Random Geometry Option

There is also a random geometry mode. If you set "Random" in the geom_types parameter when creating a lattice, the system will automatically select one geometry from the available .json files in the geometries/ folder.

➕ Adding a New Geometry

To define your own unit cell geometry:

  1. Create a .json file inside the src/geometries/ folder.
  2. Use the following structure:
{
  "name": "MyNewCell",
  "description": "A custom parametric lattice unit cell",
  "parameters": {
    "a": 0.25,
    "b": "1 - a"
  },
  "beams": [
    [0.0, 0.0, 0.0, "a", "a", "a"],
    ["a", "a", "a", "b", "b", "b"]
  ]
}

Information:

Geometries are defined in a unit cell of size 1x1x1, so the coordinates in the beams list should be normalized to this unit cell size.