TPMS, strut, and face lattices
==============================

.. currentmodule:: pyvcad_metamaterials

TPMS lattices
-------------

Every TPMS builder returns a ``pyvcad.MappedImplicitLattice`` (or a
``pyvcad.MappedStructureCollection`` for a multi-map collection) in either
``"sheet"`` or ``"solid"`` mode.

.. autofunction:: tpms

.. autodata:: TPMS_NAMES
   :no-value:

   Names accepted by :func:`tpms`: ``fischer_koch_s``, ``frd``, ``gyroid``,
   ``iwp``, ``lidinoid``, ``neovius``, ``schwarz_d``, ``schwarz_p``,
   ``split_p``.

.. autofunction:: gyroid

.. autofunction:: schwarz_p

.. autofunction:: schwarz_d

.. autofunction:: neovius

.. autofunction:: iwp

.. autofunction:: lidinoid

.. autofunction:: split_p

.. autofunction:: fischer_koch_s

.. autofunction:: frd

Strut (graph) lattices
----------------------

Every strut builder returns a ``pyvcad.MappedGraphLattice`` (or a
``pyvcad.MappedStructureCollection`` for a multi-map collection).

.. autofunction:: graph_lattice

.. autodata:: LATTICE_NAMES
   :no-value:

   Names accepted by :func:`graph_lattice`: ``bcc``, ``column``,
   ``columns``, ``cubic``, ``diamond``, ``fcc``, ``fluorite``,
   ``hex_prism_central_axis``, ``hex_prism_diamond``, ``hex_prism_edge``,
   ``hex_prism_laves``, ``hex_prism_vertex_centroid``, ``isotruss``,
   ``kelvin``, ``oct_vertex_centroid``, ``octet``, ``reentrant_3d``,
   ``reentrant_hex_prism``, ``rhombic_dodecahedron``,
   ``rotated_square_prism_edge``, ``rotated_triangular_prism_edge``,
   ``tet_oct_vertex_centroid``, ``triangular_prism_edge``,
   ``truncated_cube``, ``weaire_phelan``.

.. autofunction:: cubic

.. autofunction:: bcc

.. autofunction:: fcc

.. autofunction:: kelvin

.. autofunction:: octet

.. autofunction:: diamond

.. autofunction:: isotruss

.. autofunction:: fluorite

.. autofunction:: hex_prism_edge

.. autofunction:: reentrant_hex_prism

.. autofunction:: rhombic_dodecahedron

.. autofunction:: weaire_phelan

.. autofunction:: truncated_cube

.. autofunction:: column

.. autofunction:: columns

.. autofunction:: reentrant_3d

.. autofunction:: triangular_prism_edge

.. autofunction:: rotated_triangular_prism_edge

.. autofunction:: rotated_square_prism_edge

.. autofunction:: hex_prism_vertex_centroid

.. autofunction:: hex_prism_central_axis

.. autofunction:: hex_prism_diamond

.. autofunction:: hex_prism_laves

.. autofunction:: tet_oct_vertex_centroid

.. autofunction:: oct_vertex_centroid

.. autofunction:: reference_cell_size

.. autofunction:: hex_prism_reference_aspect_ratio

.. autofunction:: reentrant_hex_prism_reference_aspect_ratio

Face (plate and wall) lattices
------------------------------

Face builders return a ``pyvcad.MappedFaceLattice`` (or a
``pyvcad.MappedStructureCollection`` for a multi-map collection) whose
center surfaces are thickened into walls.

.. autofunction:: face_lattice

.. autodata:: FACE_LATTICE_NAMES
   :no-value:

   Names accepted by :func:`face_lattice` and :func:`face_unit_cell`: ``plate``,
   ``simple_cubic_plate``, ``body_centered_cubic_plate``,
   ``face_centered_cubic_plate``, ``cubic_octet_plate``,
   ``hexagonal_honeycomb``, ``reentrant_honeycomb``, ``square_honeycomb``,
   ``rotated_square_honeycomb``, ``triangular_honeycomb``,
   ``rotated_triangular_honeycomb``.

Plate lattices
^^^^^^^^^^^^^^

.. autofunction:: plate_lattice

.. autofunction:: simple_cubic_plate

.. autofunction:: body_centered_cubic_plate

.. autofunction:: face_centered_cubic_plate

.. autofunction:: octet_plate

.. autofunction:: cubic_octet_plate

Honeycombs
^^^^^^^^^^

Wall cells extruded along W.

.. autofunction:: hexagonal_honeycomb

.. autofunction:: reentrant_honeycomb

.. autofunction:: square_honeycomb

.. autofunction:: rotated_square_honeycomb

.. autofunction:: triangular_honeycomb

.. autofunction:: rotated_triangular_honeycomb

Face unit cells
^^^^^^^^^^^^^^^

Each builder returns a ``pyvcad.FaceUnitCell`` for :func:`face_lattice`, for
example to inspect the cell or to tag faces before tiling.

.. autofunction:: face_unit_cell

.. autofunction:: simple_cubic_plate_cell

.. autofunction:: body_centered_cubic_plate_cell

.. autofunction:: face_centered_cubic_plate_cell

.. autofunction:: cubic_octet_plate_cell

.. autofunction:: hexagonal_honeycomb_cell

.. autofunction:: reentrant_honeycomb_cell

.. autofunction:: square_honeycomb_cell

.. autofunction:: rotated_square_honeycomb_cell

.. autofunction:: triangular_honeycomb_cell

.. autofunction:: rotated_triangular_honeycomb_cell

Building graph cells from seeds and tessellations
--------------------------------------------------

These builders return the same edge lists as the catalog cells (origin-centred,
spanning ``[-0.5, 0.5]``), so their results go straight into
:func:`graph_lattice`; :meth:`PeriodicTessellation.face_cell` returns a
``pyvcad.FaceUnitCell`` for :func:`face_lattice`. See
:doc:`/guides/metamaterials/custom-unit-cells` for a walkthrough.

.. autofunction:: periodic_voronoi

.. autofunction:: periodic_bonds

.. autofunction:: tessellation

.. autodata:: TESSELLATION_NAMES
   :no-value:

   Names accepted by :func:`tessellation`: ``cube``, ``hexagonal_prism``,
   ``reentrant_hexagonal_prism``, ``triangular_prism``,
   ``rotated_triangular_prism``, ``rotated_square_prism``, ``tet_oct``,
   ``truncated_cube``.

.. autodata:: GRAPH_RULES
   :no-value:

   Rules accepted by :meth:`PeriodicTessellation.edges`: ``edges``,
   ``cell_vertex_centroid``, ``facet_vertex_centroid``, ``dual``,
   ``central_axes``.

.. autoclass:: PeriodicTessellation
   :members: edges, face_cell

.. autoclass:: Polyhedron
   :members: prism

Lattices from meshes
--------------------

.. autofunction:: mesh_lattice