locan.data.regions.region.AxisOrientedHypercuboid

class locan.data.regions.region.AxisOrientedHypercuboid(corner=(0, 0, 0), lengths=(1, 1, 1))

Bases: RegionND

Region class to define an axis-oriented n-dimensional hypercuboid.

This is a n-dimensional convex region with rectangular faces and edges that are parallel to coordinate axes. Extension in x-, y-, z-coordinates correspond to length, width, height.

Parameters:

• corner (npt.ArrayLike) – A point with shape (dimension,) that defines the lower left corner.

• lengths (npt.ArrayLike) – Array of shape(dimension,) of length values for the 1-dimensional edge vectors.

Methods

__init__([corner, lengths])
buffer(distance, **kwargs)	Extend the region perpendicular by a distance.
contains(points)	Return list of indices for all points that are inside the region of interest.
from_intervals(intervals)	Constructor for instantiating Region from list of (min, max) bounds.
intersection(other)	Returns a region representing the intersection of this region with other.
symmetric_difference(other)	Returns the union of the two regions minus any areas contained in the intersection of the two regions.
union(other)	Returns a region representing the union of this region with other.

Attributes

bounding_box	A region describing the minimum axis-aligned bounding box that encloses the original region.
bounds	Region bounds min_x, min_y, ..., max_x, max_y, .
centroid	Point coordinates for region centroid.
corner	A point that defines the lower left corner.
dimension	The region dimension.
elongation	A measure between 0 and 1 for how elongated the object is.
extent	The extent (max_x - min_x), (max_y - min_y), .
intervals	Provide bounds in a tuple (min, max) arrangement.
lengths	Array of length values for the 1-dimensional edge vectors.
max_distance	The maximum distance between any two points within the region.
points
radial_distance	Average of all absolute distances between vertices and centroid.
region_measure	Region measure, i.e. area (for 2d) or volume (for 3d).
subregion_measure	Measure of the sub-dimensional region, i.e. perimeter length (for 2d) or surface area (for 3d).
vertices	0 - dimensional elements that define the region; also called points.

property bounding_box: Self

A region describing the minimum axis-aligned bounding box that encloses the original region.

Return type:

Region

property bounds: ndarray[tuple[int, ...], dtype[float64]]

Region bounds min_x, min_y, …, max_x, max_y, … for each dimension.

Returns:

of shape (2 * dimension,)

Return type:

npt.NDArray[np.float64] | None

buffer(distance, **kwargs)

Extend the region perpendicular by a distance.

Parameters:

distance (float) – Distance by which the region is extended.

Returns:

The extended region.

Return type:

Region

property centroid: ndarray[tuple[int, ...], dtype[float64]]

Point coordinates for region centroid.

Returns:

of shape (dimension,)

Return type:

npt.NDArray[np.float64] | None

contains(points)

Return list of indices for all points that are inside the region of interest.

Parameters:

points (Union[_Buffer, _SupportsArray[dtype[Any]], _NestedSequence[_SupportsArray[dtype[Any]]], bool, int, float, complex, str, bytes, _NestedSequence[bool | int | float | complex | str | bytes]]) – Coordinates of points that are tested for being inside the specified region.

Returns:

Array with indices for all points in original point array that are within the region.

Return type:

npt.NDArray[np.int64]

property corner: ndarray[tuple[int, ...], dtype[float64]]

A point that defines the lower left corner.

Returns:

with shape (dimension,)

Return type:

npt.NDArray[np.float64]

property dimension: int

The region dimension.

Return type:

int | None

property elongation: float

A measure between 0 and 1 for how elongated the object is. It is computed as: 1 - the ratio of length of minor axis to length of major axis.

Return type:

float

property extent: ndarray[tuple[int, ...], dtype[float64]]

The extent (max_x - min_x), (max_y - min_y), … for each dimension.

Returns:

of shape (dimension,)

Return type:

npt.NDArray[np.float64] | None

classmethod from_intervals(intervals)

Constructor for instantiating Region from list of (min, max) bounds.

Parameters:

intervals (npt.ArrayLike) – The region bounds for each dimension of shape (dimension, 2)

Return type:

AxisOrientedHypercuboid

property intervals: ndarray[tuple[int, ...], dtype[float64]]

Provide bounds in a tuple (min, max) arrangement.

Returns:

((min_x, max_x), …) of shape(dimension, 2)

Return type:

npt.NDArray[np.float64]

property lengths: ndarray[tuple[int, ...], dtype[float64]]

Array of length values for the 1-dimensional edge vectors.

Returns:

of shape(dimension,)

Return type:

npt.NDArray[np.float64]

property max_distance: float

The maximum distance between any two points within the region.

Return type:

float

property points: ndarray[tuple[int, ...], dtype[float64]]

property region_measure: float

Region measure, i.e. area (for 2d) or volume (for 3d).

Return type:

float

property subregion_measure: float

Measure of the sub-dimensional region, i.e. perimeter length (for 2d) or surface area (for 3d).

Return type:

float

property vertices: ndarray[tuple[int, ...], dtype[float64]]

0 - dimensional elements that define the region; also called points.

Returns:

of shape (n_vertices, dimension)

Return type:

npt.NDArray[np.float64] | list[npt.NDArray[np.float64]]