Hexagon

class sionna.sys.Hexagon(radius: float, coord: List[int] | Tuple[int, int] | torch.Tensor, coord_type: str = 'offset', precision: Literal['single', 'double'] | None = None, device: str | None = None)

Bases: sionna.phy.object.Object

Class defining a hexagon placed in a hexagonal grid.

Parameters:

• radius (float) – Hexagon radius, defined as the distance between the hexagon center and any of its corners

• coord (List[int] | Tuple[int, int] | torch.Tensor) – Coordinates of the hexagon center within the grid with shape [2]. If coord_type is ‘euclid’, the unit of measurement is meters [m].

• coord_type (str) – Coordinate type of coord. One of ‘offset’ (default), ‘axial’, or ‘euclid’.

• precision (Literal['single', 'double'] | None) – Precision used for internal calculations and outputs. If set to None, precision is used.

• device (str | None) – Device for computation. If None, device is used.

Attributes

property coord_offset: torch.Tensor

[2], torch.int32 : Offset coordinates of the hexagon within a grid. The first (second) coordinate defines the horizontal (vertical) offset with respect to the grid center.

property coord_axial: torch.Tensor

[2], torch.int32 : Axial coordinates of the hexagon within a grid.

The basis of axial coordinates are 2D vectors \(\mathbf{b}^{(1)}=\left(\frac{3}{2}r,\frac{\sqrt{3}}{2}r \right)\), \(\mathbf{b}^{(2)}=\left(0, \sqrt{3}r \right)\). Thus, the relationship between axial coordinates \(\mathbf{a}=(a_1,a_2)\) and their corresponding Euclidean ones \(\mathbf{x}=(x_1,x_2)\) is the following:

\[\mathbf{x} = a_1 \mathbf{b}^{(1)} + a_2 \mathbf{b}^{(2)}\]

property coord_euclid: torch.Tensor

[2], torch.float : Euclidean coordinates of the hexagon within a grid.

property radius: torch.Tensor

torch.float : Hexagon radius, defined as the distance between its center and any of its corners.

Methods

corners() → torch.Tensor

Computes the Euclidean coordinates of the 6 corners of the hexagon.

Outputs:

corners – Euclidean coordinates of the 6 corners with shape [6, 2], torch.float

neighbor(axial_direction_idx: int) → sionna.sys.topology.Hexagon

Returns the neighboring hexagon over the specified axial direction.

Parameters:

axial_direction_idx (int) – Index determining the neighbor relative axial direction with respect to the current hexagon. Must be one of {0,…,5}.

Outputs:

neighbor – Hexagon – Neighboring hexagon, in the axial relative direction

coord_dict() → Dict[str, torch.Tensor]

Returns the hexagon coordinates in the form of a dictionary.

Outputs:

coord_dict – dict – Dictionary containing the three hexagon coordinates, with keys ‘euclid’, ‘offset’, ‘axial’