padne.mesh

Attributes

index_type
Mesh
Vertex
HalfEdge
Face
PolyBoundaryDistanceMap
CGALPolygon

Exceptions

MeshingException

Raised when CGAL fails to mesh a polygon due to degenerate geometry.

Classes

Vector
Point
ZeroForm	Element-wise arithmetic shared by the discrete forms.
OneForm	A discrete 1-form defined on the (h)edges of a mesh.
TwoForm	A discrete 2-form defined on the faces of a mesh.
Mesher	This class is responsible for generating a mesh from a Shapely polygon.

Module Contents

padne.mesh.index_type

class padne.mesh.Vector

dx: float

dy: float

dot(other: Vector) → float

class padne.mesh.Point

x: float

y: float

distance(other: Point) → float

to_shapely() → shapely.geometry.Point

Convert this Point to a shapely.geometry.Point.

Returns:

A shapely Point with the same coordinates

padne.mesh.Mesh

padne.mesh.Vertex

padne.mesh.HalfEdge

padne.mesh.Face

class padne.mesh.ZeroForm

Bases: _Form

Element-wise arithmetic shared by the discrete forms.

d() → OneForm

Compute the exterior derivative (gradient) of this 0-form.

For a function f on vertices, the exterior derivative df is a 1-form where: (df)[edge] = f(target_vertex) - f(source_vertex)

Returns:

A OneForm representing the gradient of this function

class padne.mesh.OneForm

Bases: _Form

A discrete 1-form defined on the (h)edges of a mesh.

class padne.mesh.TwoForm

Bases: _Form

A discrete 2-form defined on the faces of a mesh.

padne.mesh.PolyBoundaryDistanceMap

padne.mesh.CGALPolygon

exception padne.mesh.MeshingException

Bases: RuntimeError

Raised when CGAL fails to mesh a polygon due to degenerate geometry.

class padne.mesh.Mesher(config: Mesher | None = None)

This class is responsible for generating a mesh from a Shapely polygon. Works through CGAL.

class Config

Configuration parameters for mesh generation.

minimum_angle: float = 20.0

maximum_size: float = 0.6

variable_density_min_distance: float = 0.5

variable_density_max_distance: float = 3.0

variable_size_maximum_factor: float = 3.0

distance_map_quantization: float = 1.0

RELAXED = None

property is_variable_density: bool

Return True if variable density meshing is enabled.

config

poly_to_mesh(poly: shapely.geometry.Polygon, seed_points: Sequence[Point | shapely.geometry.Point] = ()) → Mesh

Convert a Shapely polygon to a triangular mesh.

Args:

poly: A Shapely polygon, potentially with holes

Returns:

A Mesh object representing the triangulated polygon