capytaine.meshes.symmetric_meshes module

class capytaine.meshes.symmetric_meshes.ReflectionSymmetricMesh(half: AbstractMesh, *, plane: str, faces_metadata: Dict[str, ndarray] | None = None, name: str | None = None)

Bases: AbstractMesh

A mesh with reflection symmetry across a plane.

This class represents a mesh that has reflection symmetry across either the xOz plane (y=0) or yOz plane (x=0). Only half of the mesh is stored, and the full mesh can be reconstructed by reflecting across the symmetry plane.

Supports nested symmetries: if the half mesh is itself a ReflectionSymmetricMesh, this represents a quarter mesh with symmetries across both planes.

Variables:

• half (AbstractMesh) – The half mesh

• plane (str) – The symmetry plane, either “xOz” or “yOz”

• faces_metadata (Dict[str, np.ndarray], optional) – Some arrays with the same first dimension (should be the number of faces of the whole mesh) storing some fields defined on all the faces of the mesh.

• name (str, optional) – Name for the mesh

Examples

>>> # Create a mesh with xOz symmetry (y=0 plane)
>>> half_mesh = Mesh(vertices=..., faces=...)
>>> symmetric_mesh = ReflectionSymmetricMesh(half=half_mesh, plane="xOz")
>>>
>>> # Create a mesh with both xOz and yOz symmetries (quarter mesh)
>>> quarter_mesh = Mesh(vertices=..., faces=...)
>>> sym_xOz = ReflectionSymmetricMesh(half=quarter_mesh, plane="xOz")
>>> sym_both = ReflectionSymmetricMesh(half=sym_xOz, plane="yOz")
>>>
>>> # Get the full merged mesh
>>> full_mesh = symmetric_mesh.merged()

clipped(*, origin, normal, name=None) → ReflectionSymmetricMesh | Mesh

copy(*, faces_metadata=None, name=None) → ReflectionSymmetricMesh

export(format, **kwargs)

extract_faces(faces_id, *, name=None) → Mesh

extract_lid(z=0.0)

property faces: ndarray

property faces_areas: ndarray

property faces_centers: ndarray

property faces_normals: ndarray

property faces_radiuses: ndarray

generate_lid(z=0.0, faces_max_radius=None, name=None)

join_meshes(*meshes, return_masks=False, name=None) → ReflectionSymmetricMesh | Mesh

merged(name=None) → Mesh

mirrored(plane: Literal['xOz', 'yOz'], *, name=None) → ReflectionSymmetricMesh

property nb_faces: int

property nb_vertices: int

property quadrature_points: ndarray

rotated_with_matrix(R, *, name=None) → Mesh

show(*, backend=None, ghost_meshes=None, **kwargs)

translated(shift, *, name=None) → ReflectionSymmetricMesh | Mesh

property vertices: ndarray

with_normal_vector_going_down(**kwargs) → ReflectionSymmetricMesh

with_quadrature(quadrature_method)

class capytaine.meshes.symmetric_meshes.RotationSymmetricMesh(wedge: AbstractMesh, n: int, *, axis: Literal['z+', 'z-'] = 'z+', faces_metadata: Dict[str, ndarray] | None = None, name: str | None = None)

Bases: AbstractMesh

A mesh with rotation symmetry around the Oz axis.

This class represents a mesh that has n-fold rotational symmetry about the z-axis. Only a wedge (1/n of the full mesh) is stored, and the full mesh can be reconstructed by rotating the wedge n times.

Supports nested symmetries: the wedge mesh can be a ReflectionSymmetricMesh for dihedral symmetry.

Variables:

• wedge (AbstractMesh) – The wedge mesh (1/n of the full mesh)

• n (int) – The rotation order (number of rotations to complete full circle)

• axis (either 'z+' or 'z-') – Only the z-axis is supported, but two possible orientations can be used. Both are equivalent, except for the ordering of the sub-meshes.

• faces_metadata (Dict[str, np.ndarray], optional) – Some arrays with the same first dimension (should be the number of faces of the whole mesh) storing some fields defined on all the faces of the mesh.

• name (str, optional) – Name for the mesh

Examples

>>> # Create a mesh with 3-fold rotation symmetry about z-axis
>>> wedge_mesh = Mesh(vertices=..., faces=...)
>>> symmetric_mesh = RotationSymmetricMesh(wedge=wedge_mesh, n=3)
>>>
>>> # Get the full merged mesh
>>> full_mesh = symmetric_mesh.merged()

clipped(*, origin, normal, name=None) → RotationSymmetricMesh | Mesh

copy(*, faces_metadata=None, name=None) → RotationSymmetricMesh

export(format, **kwargs)

extract_faces(faces_id, *, name=None) → Mesh

extract_lid(z=0.0)

property faces: ndarray

property faces_areas: ndarray

property faces_centers: ndarray

property faces_normals: ndarray

property faces_radiuses: ndarray

classmethod from_profile_points(points: ndarray, n: int, *, faces_metadata=None, name=None)

Return the mesh defined by the set of points repeated n times around the z-axis.

Points will be sorted by increasing z-coordinate before making a mesh, in order to ensure that the normal vector are outwards.

Parameters:

• points (array of shape (…, 3)) – A list of points in 3D.

• n (int) – The rotation order (number of rotations to complete full circle)

• faces_metadata (Dict[str, np.ndarray], optional) – Some arrays with the same first dimension (should be the number of faces of the whole mesh) storing some fields defined on all the faces of the mesh.

• name (str, optional) – Name for the mesh

Example

>>> meridian_points = np.array([(np.sqrt(1-z**2), 0.0, z) for z in np.linspace(-1.0, 1.0, 10)])
>>> sphere = RotationSymmetricMesh.from_profile_points(meridian_points, n=10)

generate_lid(z=0.0, faces_max_radius=None, name=None)

join_meshes(*meshes, return_masks=False, name=None) → RotationSymmetricMesh | Mesh

merged(name=None) → Mesh

mirrored(plane: Literal['xOz', 'yOz'], *, name=None) → RotationSymmetricMesh

property nb_faces: int

property nb_vertices: int

property quadrature_points: ndarray

rotated_with_matrix(R, *, name=None) → RotationSymmetricMesh | Mesh

show(*, backend=None, ghost_meshes=None, **kwargs)

translated(shift, *, name=None) → RotationSymmetricMesh | Mesh

property vertices: ndarray

with_normal_vector_going_down(**kwargs) → RotationSymmetricMesh

with_quadrature(quadrature_method)