pinnx.geometry module

This module provides geometric domains for defining the spatial and temporal extent of PDE problems. Geometries support point sampling, boundary identification, and boolean operations for complex shapes.

Core Interfaces

Base classes and key geometric constructs.

AbstractGeometry: Base class for all geometries.

Geometry: Standard geometry interface.

GeometryXTime: Combines spatial geometry with time domain for time-dependent problems.

TimeDomain: Represents the temporal dimension.

DictPointGeometry: Geometry that works with dictionary-based points with physical units.

AbstractGeometry
Geometry	Base class for defining geometries.
GeometryXTime
TimeDomain
DictPointGeometry	Convert a geometry to a dictionary geometry.

Boolean Operations

Constructive solid geometry (CSG) operations for combining geometries.

CSGUnion: Union of two geometries (A ∪ B).

CSGIntersection: Intersection of two geometries (A ∩ B).

CSGDifference: Difference of two geometries (A B).

CSGUnion	Construct an object by CSG Union.
CSGIntersection	Construct an object by CSG Intersection.
CSGDifference	Construct an object by CSG Difference.

Canonical Domains

Standard geometric shapes in 1D, 2D, 3D, and N-D.

1D: Interval

2D: Rectangle, Triangle, Polygon, Disk, Ellipse, StarShaped

3D: Cuboid, Sphere

N-D: Hypercube, Hypersphere

Interval
Rectangle
Triangle	Triangle.
Polygon	Simple polygon.
Disk
Ellipse	Ellipse.
StarShaped	Star-shaped 2d domain, i.e., a geometry whose boundary is parametrized in polar coordinates as:
Cuboid
Sphere
Hypercube
Hypersphere

Point-Based Geometry

Geometries defined by discrete point sets.

PointCloud

A geometry represented by a point cloud, i.e., a set of points in space.