microgen.shape package

Shape (microgen.shape)

class microgen.shape.Box(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), dim_x: float = 1, dim_y: float = 1, dim_z: float = 1)

Bases: BasicGeometry

Class to generate a box

_images/microgen.shape_1_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(level=0, quads=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.Capsule(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), height: float = 1, radius: float = 0.5)

Bases: BasicGeometry

Class to generate a capsule (cylinder with hemispherical ends)

_images/microgen.shape_2_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(resolution=100, theta_resolution=50, phi_resolution=50, capping=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.Cylinder(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), height: float = 1, radius: float = 0.5)

Bases: BasicGeometry

Class to generate a cylinder

_images/microgen.shape_3_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(resolution=100, capping=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.CylindricalTpms(radius: float, surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], offset: float | Callable[[ndarray, ndarray, ndarray], ndarray] = 0.0, phase_shift: Sequence[float] = (0.0, 0.0, 0.0), cell_size: float | Sequence[float] = 1.0, repeat_cell: int | Sequence[int] = 1, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), resolution: int = 20, density: float | None = None)

Bases: Tpms

Class used to generate cylindrical TPMS geometries (sheet or skeletals parts).

class microgen.shape.Ellipsoid(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), a_x: float = 1, a_y: float = 0.5, a_z: float = 0.25)

Bases: BasicGeometry

Class to generate an ellipsoid

_images/microgen.shape_4_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk() → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.ExtrudedPolygon(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), listCorners: Sequence[Tuple[float, float]] = [(1, 0), (0.5, 0.8660254037844386), (-0.5, 0.8660254037844386), (-1, 0), (-0.5, -0.8660254037844386), (0.5, -0.8660254037844386), (1, 0)], height: float = 1)

Bases: BasicGeometry

Class to generate an extruded polygon with a given list of points and a thickness

_images/microgen.shape_5_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(capping=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.Polyhedron(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), dic: Dict[str, list] = {'faces': [{'vertices': [0, 1, 2]}, {'vertices': [0, 3, 1]}, {'vertices': [0, 2, 3]}, {'vertices': [1, 2, 3]}], 'vertices': [(1.0, 1.0, 1.0), (1.0, -1.0, -1.0), (-1.0, 1.0, -1.0), (-1.0, -1.0, 1.0)]})

Bases: BasicGeometry

Class to generate a Polyhedron with a given set of faces and vertices

_images/microgen.shape_6_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk() → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.Sphere(center: Tuple[float, float, float] = (0, 0, 0), radius: float = 1)

Bases: BasicGeometry

Class to generate a sphere

_images/microgen.shape_7_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(theta_resolution=50, phi_resolution=50) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

class microgen.shape.SphericalTpms(radius: float, surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], offset: float | Callable[[ndarray, ndarray, ndarray], ndarray] = 0.0, phase_shift: Sequence[float] = (0.0, 0.0, 0.0), cell_size: float | Sequence[float] = 1.0, repeat_cell: int | Sequence[int] = 1, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), resolution: int = 20, density: float | None = None)

Bases: Tpms

Class used to generate spherical TPMS geometries (sheet or skeletals parts).

class microgen.shape.Tpms(surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], offset: float | Callable[[ndarray, ndarray, ndarray], ndarray] = 0.0, phase_shift: Sequence[float] = (0.0, 0.0, 0.0), cell_size: float | Sequence[float] = 1.0, repeat_cell: int | Sequence[int] = 1, resolution: int = 20, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), density: float | None = None)

Bases: BasicGeometry

Class to generate Triply Periodical Minimal Surfaces (TPMS) geometry from a given mathematical function, with given offset

functions available :
generate(type_part: Literal['sheet', 'lower skeletal', 'upper skeletal', 'surface'] = 'sheet', smoothing: int = 0, verbose: bool = True, algo_resolution: int | None = None) → Shape
Parameters:

  • type_part – part of the TPMS desired (‘sheet’, ‘lower skeletal’, ‘upper skeletal’ or ‘surface’)

  • smoothing – smoothing loop iterations

  • verbose – display progressbar of the conversion to CadQuery object

  • algo_resolution – if offset must be computed to fit density, resolution of the temporary TPMS used to compute the offset

Returns:

CadQuery Shape object of the required TPMS part

generateVtk(type_part: Literal['sheet', 'lower skeletal', 'upper skeletal', 'surface'], algo_resolution: int | None = None) → PolyData
Parameters:

  • type_part – part of the TPMS desireds

  • algo_resolution – if offset must be computed to fit density, resolution of the temporary TPMS used to compute the offset

Returns:

VTK PolyData object of the required TPMS part

property lower_skeletal: PolyData

Returns lower skeletal part

classmethod offset_from_density(surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], part_type: Literal['sheet', 'lower skeletal', 'upper skeletal'], density: float | Literal['max'] = 'max', resolution: int = 20) → float

Returns the offset corresponding to the required density for the specified part of the given surface_function.

Parameters:

  • surface_function – tpms function

  • part_type – type of the part (sheet, lower skeletal or upper skeletal)

  • density – Required density, 0.5 for 50%

  • resolution – resolution of the tpms used to compute the offset

Returns:

corresponding offset value

property sheet: PolyData

Returns sheet part

property skeletals: Tuple[PolyData, PolyData]

Returns both skeletal parts

property surface: PolyData

Returns isosurface f(x, y, z) = 0

property upper_skeletal: PolyData

Returns upper skeletal part

vtk_lower_skeletal() → PolyData
vtk_sheet() → PolyData
vtk_upper_skeletal() → PolyData
microgen.shape.newGeometry(shape: str, param_geom: Dict[str, Any], center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0)) → BasicGeometry

Creates a new basic geometry with given shape and geometrical parameters

Parameters:

  • shape – name of the geometry

  • param_geom – dictionary with required geometrical parameters

  • center – center

  • orientation – orientation

Return geometry:

BasicGeometry

Basic Geometry (microgen.shape.basicGeometry)

class microgen.shape.basicGeometry.BasicGeometry(shape: str, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0))

Bases: object

BasicGeometry class to manage shapes

Parameters:

  • shape – name of the shape

  • center – center

  • orientation – orientation

generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk() → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

numInstances = 0

Box (microgen.shape.box)

class microgen.shape.box.Box(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), dim_x: float = 1, dim_y: float = 1, dim_z: float = 1)

Bases: BasicGeometry

Class to generate a box

_images/microgen.shape_8_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(level=0, quads=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

Capsule (microgen.shape.capsule)

class microgen.shape.capsule.Capsule(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), height: float = 1, radius: float = 0.5)

Bases: BasicGeometry

Class to generate a capsule (cylinder with hemispherical ends)

_images/microgen.shape_9_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(resolution=100, theta_resolution=50, phi_resolution=50, capping=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

Cylinder (microgen.shape.cylinder)

class microgen.shape.cylinder.Cylinder(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), height: float = 1, radius: float = 0.5)

Bases: BasicGeometry

Class to generate a cylinder

_images/microgen.shape_10_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(resolution=100, capping=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

Ellipsoid (microgen.shape.ellipsoid)

class microgen.shape.ellipsoid.Ellipsoid(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), a_x: float = 1, a_y: float = 0.5, a_z: float = 0.25)

Bases: BasicGeometry

Class to generate an ellipsoid

_images/microgen.shape_11_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk() → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

Extruded Polygon (microgen.shape.extrudedPolygon)

class microgen.shape.extrudedPolygon.ExtrudedPolygon(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), listCorners: Sequence[Tuple[float, float]] = [(1, 0), (0.5, 0.8660254037844386), (-0.5, 0.8660254037844386), (-1, 0), (-0.5, -0.8660254037844386), (0.5, -0.8660254037844386), (1, 0)], height: float = 1)

Bases: BasicGeometry

Class to generate an extruded polygon with a given list of points and a thickness

_images/microgen.shape_12_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(capping=True) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

Polyhedron (microgen.shape.polyhedron)

class microgen.shape.polyhedron.Polyhedron(center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), dic: Dict[str, list] = {'faces': [{'vertices': [0, 1, 2]}, {'vertices': [0, 3, 1]}, {'vertices': [0, 2, 3]}, {'vertices': [1, 2, 3]}], 'vertices': [(1.0, 1.0, 1.0), (1.0, -1.0, -1.0), (-1.0, 1.0, -1.0), (-1.0, -1.0, 1.0)]})

Bases: BasicGeometry

Class to generate a Polyhedron with a given set of faces and vertices

_images/microgen.shape_13_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk() → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

microgen.shape.polyhedron.read_obj(filename: str)

Reads vertices and faces from obj format file for polyhedron

Sphere (microgen.shape.sphere)

class microgen.shape.sphere.Sphere(center: Tuple[float, float, float] = (0, 0, 0), radius: float = 1)

Bases: BasicGeometry

Class to generate a sphere

_images/microgen.shape_14_0.png
generate() → Shape

Generates the CAD shape

Returns:

cq.Shape

generateVtk(theta_resolution=50, phi_resolution=50) → PolyData

Generates the vtk mesh of the shape

Returns:

pv.PolyData

TPMS (microgen.shape.tpms)

class microgen.shape.tpms.CylindricalTpms(radius: float, surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], offset: float | Callable[[ndarray, ndarray, ndarray], ndarray] = 0.0, phase_shift: Sequence[float] = (0.0, 0.0, 0.0), cell_size: float | Sequence[float] = 1.0, repeat_cell: int | Sequence[int] = 1, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), resolution: int = 20, density: float | None = None)

Bases: Tpms

Class used to generate cylindrical TPMS geometries (sheet or skeletals parts).

class microgen.shape.tpms.SphericalTpms(radius: float, surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], offset: float | Callable[[ndarray, ndarray, ndarray], ndarray] = 0.0, phase_shift: Sequence[float] = (0.0, 0.0, 0.0), cell_size: float | Sequence[float] = 1.0, repeat_cell: int | Sequence[int] = 1, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), resolution: int = 20, density: float | None = None)

Bases: Tpms

Class used to generate spherical TPMS geometries (sheet or skeletals parts).

class microgen.shape.tpms.Tpms(surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], offset: float | Callable[[ndarray, ndarray, ndarray], ndarray] = 0.0, phase_shift: Sequence[float] = (0.0, 0.0, 0.0), cell_size: float | Sequence[float] = 1.0, repeat_cell: int | Sequence[int] = 1, resolution: int = 20, center: Tuple[float, float, float] = (0, 0, 0), orientation: Tuple[float, float, float] = (0, 0, 0), density: float | None = None)

Bases: BasicGeometry

Class to generate Triply Periodical Minimal Surfaces (TPMS) geometry from a given mathematical function, with given offset

functions available :
generate(type_part: Literal['sheet', 'lower skeletal', 'upper skeletal', 'surface'] = 'sheet', smoothing: int = 0, verbose: bool = True, algo_resolution: int | None = None) → Shape
Parameters:

  • type_part – part of the TPMS desired (‘sheet’, ‘lower skeletal’, ‘upper skeletal’ or ‘surface’)

  • smoothing – smoothing loop iterations

  • verbose – display progressbar of the conversion to CadQuery object

  • algo_resolution – if offset must be computed to fit density, resolution of the temporary TPMS used to compute the offset

Returns:

CadQuery Shape object of the required TPMS part

generateVtk(type_part: Literal['sheet', 'lower skeletal', 'upper skeletal', 'surface'], algo_resolution: int | None = None) → PolyData
Parameters:

  • type_part – part of the TPMS desireds

  • algo_resolution – if offset must be computed to fit density, resolution of the temporary TPMS used to compute the offset

Returns:

VTK PolyData object of the required TPMS part

property lower_skeletal: PolyData

Returns lower skeletal part

classmethod offset_from_density(surface_function: Callable[[ndarray, ndarray, ndarray], ndarray], part_type: Literal['sheet', 'lower skeletal', 'upper skeletal'], density: float | Literal['max'] = 'max', resolution: int = 20) → float

Returns the offset corresponding to the required density for the specified part of the given surface_function.

Parameters:

  • surface_function – tpms function

  • part_type – type of the part (sheet, lower skeletal or upper skeletal)

  • density – Required density, 0.5 for 50%

  • resolution – resolution of the tpms used to compute the offset

Returns:

corresponding offset value

property sheet: PolyData

Returns sheet part

property skeletals: Tuple[PolyData, PolyData]

Returns both skeletal parts

property surface: PolyData

Returns isosurface f(x, y, z) = 0

property upper_skeletal: PolyData

Returns upper skeletal part

vtk_lower_skeletal() → PolyData
vtk_sheet() → PolyData
vtk_upper_skeletal() → PolyData
microgen.shape.surface_functions.fischerKochS(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[cos(2 x) sin(y) cos(z) + cos(x) cos(2 y) sin(z) + sin(x) cos(y) cos(2 z) = 0\]
_images/microgen.shape_16_0.png
microgen.shape.surface_functions.gyroid(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[sin(x) cos(y) + sin(y) cos(z) + sin(z) cos(x) = 0\]
_images/microgen.shape_17_0.png
microgen.shape.surface_functions.honeycomb(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[sin(x) cos(y) + sin(y) + cos(z) = 0\]
_images/microgen.shape_18_0.png
microgen.shape.surface_functions.honeycomb_gyroid(x: float, y: float, z: float) → float
\[sin(x) cos(y) + sin(y) + cos(x) = 0\]
_images/microgen.shape_19_0.png
microgen.shape.surface_functions.honeycomb_lidinoid(x: float, y: float, z: float) → float
\[1.1 (sin(2 x) cos(y) + sin(2 y) sin(x) + cos(x) sin(y)) - (cos(2 x) cos(2 y) + cos(2 y) + cos(2 x)) = 0\]
_images/microgen.shape_20_0.png
microgen.shape.surface_functions.honeycomb_schoenIWP(x: float, y: float, z: float) → float
\[cos(x) cos(y) + cos(y) + cos(x) = 0\]
_images/microgen.shape_21_0.png
microgen.shape.surface_functions.honeycomb_schwarzD(x: float, y: float, z: float) → float
\[cos(x) cos(y) + sin(x) sin(y) + sin(x) cos(y) + cos(x) sin(y) = 0\]
_images/microgen.shape_22_0.png
microgen.shape.surface_functions.honeycomb_schwarzP(x: float, y: float, z: float) → float
\[cos(x) + cos(y) = 0\]
_images/microgen.shape_23_0.png
microgen.shape.surface_functions.lidinoid(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[0.5 (sin(2 x) cos(y) sin(z) + sin(2 y) cos(z) sin(x) + sin(2 z) cos(x) sin(y)) - 0.5 (cos(2 x) cos(2 y) + cos(2 y) cos(2 z) + cos(2 z) cos(2 x)) + 0.3 = 0\]
_images/microgen.shape_24_0.png
microgen.shape.surface_functions.neovius(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[3 cos(x) + cos(y) + cos(z) + 4 cos(x) cos(y) cos(z) = 0\]
_images/microgen.shape_25_0.png
microgen.shape.surface_functions.pmy(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[2 cos(x) cos(y) cos(z) + sin(2 x) sin(y) + sin(x) sin(2 z) + sin(2 y) sin(z) = 0\]
_images/microgen.shape_26_0.png
microgen.shape.surface_functions.schoenFRD(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[4 cos(x) cos(y) cos(z) - (cos(2 x) cos(2 y) + cos(2 y) cos(2 z) + cos(2 z) cos(2 x)) = 0\]
_images/microgen.shape_27_0.png
microgen.shape.surface_functions.schoenIWP(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[2 (cos(x) cos(y) + cos(y) cos(z) + cos(z) cos(x)) - (cos(2 x) + cos(2 y) + cos(2 z)) = 0\]
_images/microgen.shape_28_0.png
microgen.shape.surface_functions.schwarzD(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[sin(x) sin(y) sin(z) + sin(x) cos(y) cos(z) + cos(x) sin(y) cos(z) + cos(x) cos(y) sin(z) = 0\]
_images/microgen.shape_29_0.png
microgen.shape.surface_functions.schwarzP(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[cos(x) + cos(y) + cos(z) = 0\]
_images/microgen.shape_30_0.png
microgen.shape.surface_functions.split_p(x: ndarray, y: ndarray, z: ndarray) → ndarray
\[1.1 (sin(2 x) cos(y) sin(z) + sin(2 y) cos(z) sin(x) + sin(2 z) cos(x) sin(y)) - 0.2 (cos(2 x) cos(2 y) + cos(2 y) cos(2 z) + cos(2 z) cos(2 x)) - 0.4 (cos(2 x) + cos(2 y) + cos(2 z)) = 0\]
_images/microgen.shape_31_0.png