4.6.3 pde.tools.cuboid module

An n-dimensional, axes-aligned cuboid.

This module defines the Cuboid class, which represents an n-dimensional cuboid that is aligned with the axes of a Cartesian coordinate system.

class Cuboid(pos, size, mutable=True)

Bases: object

Class that represents a cuboid in \(n\) dimensions.

Defines a cuboid from a position and a size vector.

Parameters:

• pos (list) – The position of the lower left corner. The length of this list determines the dimensionality of space

• size (list) – The size of the cuboid along each dimension.

• mutable (bool) – Flag determining whether the cuboid parameters can be changed

property bounds: tuple[tuple[float, float], ...]

buffer(amount=0, inplace=False)

Dilate the cuboid by a certain amount in all directions.

Parameters:

amount (FloatOrArray)

Return type:

Cuboid

property centroid

contains_point(points)

Returns a True when points are within the Cuboid.

Parameters:

points (ndarray) – List of point coordinates

Returns:

list of booleans indicating which points are inside

Return type:

ndarray

copy()

Return type:

Cuboid

property corners: tuple[NumericArray, NumericArray]

Return coordinates of two extreme corners defining the cuboid.

property diagonal: float

Returns the length of the diagonal.

property dim: int

classmethod from_bounds(bounds, **kwargs)

Create cuboid from bounds.

Parameters:

bounds (list) – Two dimensional array of axes bounds

Returns:

cuboid with positive size

Return type:

Cuboid

classmethod from_centerpoint(centerpoint, size, **kwargs)

Create cuboid from two points.

Parameters:

• centerpoint (list) – Coordinates of the center

• size (list) – Size of the cuboid

Returns:

cuboid with positive size

Return type:

Cuboid

classmethod from_points(p1, p2, **kwargs)

Create cuboid from two points.

Parameters:

• p1 (list) – Coordinates of first corner point

• p2 (list) – Coordinates of second corner point

Returns:

cuboid with positive size

Return type:

Cuboid

property mutable: bool

property size: NumericArray

property surface_area: float

Surface area of a cuboid in \(n\) dimensions.

The surface area is the volume of the (\(n-1\))-dimensional hypercubes that bound the current cuboid:

• \(n=1\): the number of end points (2)

• \(n=2\): the perimeter of the rectangle

• \(n=3\): the surface area of the cuboid

property vertices: list[list[float]]

Return the coordinates of all the corners.

property volume: float

asanyarray_flags(data, dtype=None, writeable=True)

Turns data into an array and sets the respective flags.

A copy is only made if necessary

Parameters:

• data (ndarray) – numpy array that whose flags are adjusted

• dtype (DTypeLike) – the resulant dtype

• writeable (bool) – Flag determining whether the results is writable

Returns:

array with same data as data but with flags adjusted.

Return type:

ndarray