Metamaterials

OpenVCAD represents architected materials by separating a reusable unit cell from the cell map that places and deforms its repetitions. The same TPMS or graph cell can therefore be tiled in a rectangular block, graded across a part, clipped by ordinary geometry, or mapped onto CAD faces without changing its topology.

This section assumes you have completed Getting Started and Functional Grading. It is written for researchers and engineers who already work with lattice structures and want to understand OpenVCAD’s map-first Python workflow.

Guide sequence

Guide	Focus	Primary Python interfaces
Concepts and representation	Unit cells, TPMS fields, graph cells, and the role of a CellMap	ImplicitUnitCell, GraphUnitCell, CellMap
TPMS and lattice catalog	Built-in cells, their parameters, and filling ordinary geometry	tpms, graph_lattice, named builders
Custom unit cells	Build graph and implicit cells with Python, then tile and conformally map them	GraphUnitCell, ImplicitUnitCell, graph_lattice, tpms
Stochastic Voronoi and Delaunay lattices	Build irregular beam and plate lattices from graded point distributions inside implicit hosts	sample_points_in_host, voronoi_graph_lattice, delaunay_graph_lattice, plate builders
Functionally graded geometry	Composing scalar and vector fields to grade thickness, radius, spacing, and topology	FloatAttribute, Vec3Attribute, DerivedFloatAttribute, CellMap
Attribute modeling	Named scalar, vector, color, and material fields in map and component scopes	set_attribute, mapped coordinates, struts, joints, plates, shell
Cylindrical and spherical cell maps	Place familiar unit cells in ideal pipes, sleeves, spherical shells, and bands without CAD	cylindrical_cell_map, spherical_cell_map
Conformal mapping CAD surfaces	CAD authoring, face selection, and curved cell maps from exact surfaces	CADModel, cell_map_from_cad_face, cell_map_between_cad_faces
Conformal mapping triangle meshes	Flattened triangle-mesh patches, trimming to the true boundary, and mesh/CAD pairing	TriangleMeshSurface, cell_map_from_surface, cell_map_between_surfaces
Heterogeneous conformal lattices	Sharp, mixed, and overlapping topology regions on one shared map	Intersection, Union, Mix, CellMap
Geometric characterization	Density, surface, channel, section, connectivity, topology, and graph metrics	properties.characterize, properties.characterize_graph_cell

Read the concepts page first if the map-first representation is new to you. Geometry grading and attribute modeling are separate workflows and can be used independently; the conformal guides build on both.

Metamaterials guides

• Concepts and representation
  • Unit cells describe topology
  • Cell maps describe layout
  • Mapped cells become ordinary OpenVCAD nodes
• TPMS and lattice catalog
  • Build a finite rectangular map
  • TPMS catalog
  • Graph lattice catalog
  • Face and plate lattice catalog
  • Fill ordinary geometry
  • Parameter summary
• Custom unit cells
  • The custom-cell workflow
  • Build a graph cell from vertices and edges
  • Generate a graph cell with Python
  • Build a custom implicit cell
  • Reuse the cells on curved maps
  • A practical first-pass checklist
  • Run all companion examples
• Stochastic Voronoi and Delaunay lattices
  • The workflow
  • Choose a family and a geometry form
  • Grade cell size with point density
  • Compare Voronoi and Delaunay beams
  • Open and closed boundaries
  • Grade beam thickness and joint size
  • Round strut junctions with member blending
  • Build stochastic plate lattices
  • Blend the finished lattice into a frame
  • Inspect prepared topology
  • A practical starting checklist
• Functionally graded metamaterial geometry
  • Compose scalar attributes
  • Grade TPMS wall thickness
  • Change cell spacing
  • Grade beams, joints, faces, and plates
  • Compose vector attributes
  • Coordinates follow the geometry that uses them
  • Choose coordinates from the CellMap
  • Express a movement in cell units
  • Use one control for geometry and sampled data
  • Mix unit cells with a scalar control
• Attribute modeling for metamaterials
  • The arrangement tools
  • Example 1: arrange gradients on a TPMS
  • Example 2: assign and grade individual struts
  • Example 3: carry the arrangements onto a conformal lattice
  • Choosing the pattern
  • Run and inspect the examples
• Cylindrical and spherical cell maps
  • Why map shape matters
  • Wrap a gyroid around a pipe
  • Rectangular or cylindrical?
  • Build a spherical protective shell
  • Rectangular or spherical?
  • Native map or surface map?
  • A few practical checks
  • Next steps
• Conformal mapping CAD surfaces
  • Install the optional CAD authoring stack
  • How a face becomes a cell map
  • Author and select a CadQuery face
  • Map between two faces
  • Import STEP and select a face
  • Create other surface shapes
  • Validation is always final
• Map lattices onto triangle meshes
  • What the patch must be
  • How the patch becomes a chart
  • Trimming to the true boundary
  • Standing the lattice off the surface
  • Sealing the cropped edge with a rim
  • Choosing the chart orientation
  • Map a procedural patch
  • Select a region of an imported mesh
  • Pair a mesh with a CAD surface
  • Limitations and troubleshooting
• Heterogeneous conformal lattices
  • Build sharp topology regions
  • Mix compatible topology fields smoothly
  • Connect incompatible topologies with overlap
  • Keep the shared layout on CAD surfaces
  • Choose sharp clipping, field mixing, or overlap
• Geometric characterization
  • Characterize any OpenVCAD design
  • What the report contains
  • Read directional cross-sections
  • Characterize a graph unit cell exactly
  • Control accuracy with voxel_size