# landlab.graph.framed_voronoi package#

## landlab.graph.framed_voronoi.dual_framed_voronoi module#

Implement the DualFramedVoronoiGraph

@author sebastien lenard @date 2022, Aug

class DualFramedVoronoiGraph(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Bases: `DualGraph`, `FramedVoronoiGraph`

Graph of a unstructured grid of Voronoi Delaunay cells and irregular patches. It is a special type of VoronoiDelaunay graph in which the initial set of points is arranged in a fixed lattice (e.g. like a rectangular raster grid) named here “layout” and the core points are then moved aroung their initial position by a random distance, lower than a certain threshold.

Examples

```>>> from landlab.graph import DualFramedVoronoiGraph
```
```>>> graph = DualFramedVoronoiGraph((3, 3), seed=200)
>>> graph.number_of_nodes
9
```
```>>> graph.x_of_node[2:4]
array([ 2.,  0.])
>>> graph.y_of_node[2:4]
array([ 0.   ,  0.749])
>>> graph.y_of_node
1.2509999999999999
```

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If float, same spacing at x and y.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, there may not be a node present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according to their position.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

DualFramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import DualFramedVoronoiGraph
>>> graph = DualFramedVoronoiGraph((3, 2), xy_spacing=1.0)
>>> graph.number_of_nodes
6
```
__init__(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If float, same spacing at x and y.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, there may not be a node present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according to their position.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

DualFramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import DualFramedVoronoiGraph
>>> graph = DualFramedVoronoiGraph((3, 2), xy_spacing=1.0)
>>> graph.number_of_nodes
6
```

`Graph.adjacent_nodes_at_node`

property angle_of_face#

Get the angle of each face.

`Graph.angle_of_link`

property area_of_cell#

Get the area of each cell.

`Graph.area_of_patch`

property cells_at_corner#

Get the cells that touch each corner.

`Graph.patches_at_node`

property cells_at_face#

Get the cells on either side of each face.

`Graph.patches_at_link`

`Graph.node_at_link_head`

property corner_at_face_tail#

Get corners at face tail.

`Graph.node_at_link_tail`

property corner_layout#
property corner_x#
property corner_y#
property corners#

Get identifier for each corner.

`Graph.nodes`

property corners_at_bottom_edge#
property corners_at_cell#

Get the corners that define a cell.

`Graph.nodes_at_patch`

property corners_at_face#

Get corners at either end of faces.

`Graph.nodes_at_link`

property corners_at_left_edge#
property corners_at_right_edge#
property corners_at_top_edge#
property face_dirs_at_corner#

Get directions of faces touching a corner.

`Graph.link_dirs_at_node`

property faces_at_cell#

Get the faces that define a cell.

`Graph.links_at_patch`

property faces_at_corner#

Get faces touching a corner.

`Graph.links_at_node`

property length_of_face#

Get the length of faces.

`Graph.length_of_link`

property midpoint_of_face#

Get the middle of faces.

`Graph.midpoint_of_link`

property number_of_cells#

Get the number of cells.

`Graph.number_of_patches`

property number_of_corners#

Get total number of corners.

`Graph.number_of_nodes`

property number_of_faces#

`Graph.number_of_links`

property perimeter_corners#
property unit_vector_at_corner#

Get a unit vector for each corner.

`Graph.unit_vector_at_node`

property unit_vector_at_face#

Make arrays to store the unit vectors associated with each face.

`Graph.unit_vector_at_link`

property x_of_corner#

Get x-coordinate of corner.

`Graph.x_of_node`

property xy_of_cell#

Get the centroid of each cell.

`Graph.xy_of_patch`

property xy_of_corner#

Get x and y-coordinates of corner.

`Graph.xy_of_node`

property xy_of_face#
property y_of_corner#

Get y-coordinate of corner.

`Graph.y_of_node`

## landlab.graph.framed_voronoi.framed_voronoi module#

Implementation of the FramedVoronoiGraph and its static layout: HorizontalRectVoronoiGraph. This pattern is inspired from the developments of the HexModelGrid

Code author: sebastien lenard

class FramedVoronoiGraph(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Bases: `DelaunayGraph`

VoronoiDelaunay graph based on a fixed lattice.

Graph of an unstructured grid of Voronoi Delaunay cells and irregular patches. It is a special type of :class`~.VoronoiDelaunayGraph` in which the initial set of points is arranged in a fixed lattice (e.g. like a `RasterModelGrid`) named here “layout” and the core points are then moved from their initial position by a random distance, lower than a certain threshold.

Examples

```>>> from landlab.graph import FramedVoronoiGraph
```
```>>> graph = FramedVoronoiGraph((3, 3), seed=200)
>>> graph.number_of_nodes
9
```
```>>> graph.x_of_node[2:4]
array([ 2.,  0.])
>>> graph.y_of_node[2:4]
array([ 0.   ,  0.749])
>>> graph.y_of_node
1.2509999999999999
```
```>>> graph.number_of_links
16
>>> graph.number_of_patches
8
```

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If `float`, same spacing x and y spacing.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, a node may not be present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according certain their positions. Currently not used.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

FramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import FramedVoronoiGraph
>>> graph = FramedVoronoiGraph((3, 2))
>>> graph.number_of_nodes
6
```
__init__(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If `float`, same spacing x and y spacing.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, a node may not be present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according certain their positions. Currently not used.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

FramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import FramedVoronoiGraph
>>> graph = FramedVoronoiGraph((3, 2))
>>> graph.number_of_nodes
6
```
property node_layout#
property nodes_at_bottom_edge#
property nodes_at_left_edge#
property nodes_at_right_edge#
property nodes_at_top_edge#
property orientation#
property perimeter_nodes#

Get nodes on the convex hull of a Graph.

Examples

```>>> import numpy as np
>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> np.sort(graph.perimeter_nodes)
array([0, 2, 3, 5])
```
property shape#
property xy_spacing#
class HorizontalRectVoronoiGraph[source]#

Bases: `object`

The horizontal rectangular frame for the FramedVoronoiGraph.

static corner_nodes(shape)[source]#
Parameters:

shape (tuple of int) – Number of rows and number of columns

Returns:

Ids of the corner nodes

Return type:

ndarray of int

Examples

```>>> from landlab.graph.framed_voronoi.framed_voronoi import HorizontalRectVoronoiGraph
>>> HorizontalRectVoronoiGraph.corner_nodes((3, 4))
(11, 8, 0, 3)
```
static nodes_at_edge(shape)[source]#
Parameters:

shape (tuple of int) – Number of rows and number of columns

Returns:

right, top, left, bottom – For each edge give the ids of the nodes present at the edge

Return type:

ndarray of int

Examples

```>>> from landlab.graph.framed_voronoi.framed_voronoi import HorizontalRectVoronoiGraph
>>> HorizontalRectVoronoiGraph.nodes_at_edge((3, 3))
(array([2, 5]), array([8, 7]), array([6, 3]), array([0, 1]))
```
static number_of_nodes(shape)[source]#
Parameters:

shape (tuple of int) – Number of rows and number of columns

Returns:

Number of nodes

Return type:

int

Examples

```>>> from landlab.graph.framed_voronoi.framed_voronoi import HorizontalRectVoronoiGraph
>>> HorizontalRectVoronoiGraph.number_of_nodes((3, 2))
6
```
static number_of_perimeter_nodes(shape)[source]#
Parameters:

shape (tuple of int) – Number of rows and number of columns

Returns:

Number of perimeter nodes

Return type:

int

Examples

```>>> from landlab.graph.framed_voronoi.framed_voronoi import HorizontalRectVoronoiGraph
>>> HorizontalRectVoronoiGraph.number_of_perimeter_nodes((3, 4))
10
```
static perimeter_nodes(shape)[source]#
Parameters:

shape (tuple of int) – Number of rows and number of columns

Returns:

Ids of the perimeter nodes

Return type:

ndarray of int

Examples

```>>> from landlab.graph.framed_voronoi.framed_voronoi import HorizontalRectVoronoiGraph
>>> HorizontalRectVoronoiGraph.perimeter_nodes((3, 3))
array([2, 5, 8, 7, 6, 3, 0, 1])
```
static xy_of_node(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), xy_min_spacing=(0.5, 0.5), seed=200)[source]#

The x and y coordinates of the graph’s nodes.

Calculation of the x-y coordinates is done following these steps:

1. Generate a rectangular, regular meshgrid.

2. Move the coordinates of the core nodes over a random distance around their initial position, within a threshold calculated from xy_spacing and xy_min_spacing.

3. Rectify the y-coordinates of the nodes of the left and right to ensure that the leftmost node of a row has a lower y than the rightmost node. This ensures that the ids of these nodes are not modified by subsequent sorting operations on the graph and make it possible to get the perimeter nodes in simple way.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If `float`, same spacing at x and y.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, a node may not be present at this location.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their initial positions cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2`. If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

x_of_node, y_of_node – The arrays of x and y coordinates.

Return type:

ndarray of float

Examples

```>>> from landlab.graph.framed_voronoi.framed_voronoi import HorizontalRectVoronoiGraph
```
```>>> x_of_node, y_of_node = HorizontalRectVoronoiGraph.xy_of_node((3, 3), seed=200)
```

Coordinates of the lower left node,

```>>> x_of_node, y_of_node
(0.0, 0.0)
```

x coordinates of the left and right edges,

```>>> x_of_node, x_of_node
(0.0, 2.0)
```

y coordinate of the middle row of the left edge,

```>>> y_of_node
0.749
```

## Module contents#

class DualFramedVoronoiGraph(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Bases: `DualGraph`, `FramedVoronoiGraph`

Graph of a unstructured grid of Voronoi Delaunay cells and irregular patches. It is a special type of VoronoiDelaunay graph in which the initial set of points is arranged in a fixed lattice (e.g. like a rectangular raster grid) named here “layout” and the core points are then moved aroung their initial position by a random distance, lower than a certain threshold.

Examples

```>>> from landlab.graph import DualFramedVoronoiGraph
```
```>>> graph = DualFramedVoronoiGraph((3, 3), seed=200)
>>> graph.number_of_nodes
9
```
```>>> graph.x_of_node[2:4]
array([ 2.,  0.])
>>> graph.y_of_node[2:4]
array([ 0.   ,  0.749])
>>> graph.y_of_node
1.2509999999999999
```

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If float, same spacing at x and y.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, there may not be a node present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according to their position.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

DualFramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import DualFramedVoronoiGraph
>>> graph = DualFramedVoronoiGraph((3, 2), xy_spacing=1.0)
>>> graph.number_of_nodes
6
```
__init__(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If float, same spacing at x and y.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, there may not be a node present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according to their position.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

DualFramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import DualFramedVoronoiGraph
>>> graph = DualFramedVoronoiGraph((3, 2), xy_spacing=1.0)
>>> graph.number_of_nodes
6
```

`Graph.adjacent_nodes_at_node`

property angle_of_face#

Get the angle of each face.

`Graph.angle_of_link`

property area_of_cell#

Get the area of each cell.

`Graph.area_of_patch`

property cells_at_corner#

Get the cells that touch each corner.

`Graph.patches_at_node`

property cells_at_face#

Get the cells on either side of each face.

`Graph.patches_at_link`

`Graph.node_at_link_head`

property corner_at_face_tail#

Get corners at face tail.

`Graph.node_at_link_tail`

property corner_layout#
property corner_x#
property corner_y#
property corners#

Get identifier for each corner.

`Graph.nodes`

property corners_at_bottom_edge#
property corners_at_cell#

Get the corners that define a cell.

`Graph.nodes_at_patch`

property corners_at_face#

Get corners at either end of faces.

`Graph.nodes_at_link`

property corners_at_left_edge#
property corners_at_right_edge#
property corners_at_top_edge#
property face_dirs_at_corner#

Get directions of faces touching a corner.

`Graph.link_dirs_at_node`

property faces_at_cell#

Get the faces that define a cell.

`Graph.links_at_patch`

property faces_at_corner#

Get faces touching a corner.

`Graph.links_at_node`

property length_of_face#

Get the length of faces.

`Graph.length_of_link`

property midpoint_of_face#

Get the middle of faces.

`Graph.midpoint_of_link`

property number_of_cells#

Get the number of cells.

`Graph.number_of_patches`

property number_of_corners#

Get total number of corners.

`Graph.number_of_nodes`

property number_of_faces#

`Graph.number_of_links`

property perimeter_corners#
property unit_vector_at_corner#

Get a unit vector for each corner.

`Graph.unit_vector_at_node`

property unit_vector_at_face#

Make arrays to store the unit vectors associated with each face.

`Graph.unit_vector_at_link`

property x_of_corner#

Get x-coordinate of corner.

`Graph.x_of_node`

property xy_of_cell#

Get the centroid of each cell.

`Graph.xy_of_patch`

property xy_of_corner#

Get x and y-coordinates of corner.

`Graph.xy_of_node`

property xy_of_face#
property y_of_corner#

Get y-coordinate of corner.

`Graph.y_of_node`

class FramedVoronoiGraph(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Bases: `DelaunayGraph`

VoronoiDelaunay graph based on a fixed lattice.

Graph of an unstructured grid of Voronoi Delaunay cells and irregular patches. It is a special type of :class`~.VoronoiDelaunayGraph` in which the initial set of points is arranged in a fixed lattice (e.g. like a `RasterModelGrid`) named here “layout” and the core points are then moved from their initial position by a random distance, lower than a certain threshold.

Examples

```>>> from landlab.graph import FramedVoronoiGraph
```
```>>> graph = FramedVoronoiGraph((3, 3), seed=200)
>>> graph.number_of_nodes
9
```
```>>> graph.x_of_node[2:4]
array([ 2.,  0.])
>>> graph.y_of_node[2:4]
array([ 0.   ,  0.749])
>>> graph.y_of_node
1.2509999999999999
```
```>>> graph.number_of_links
16
>>> graph.number_of_patches
8
```

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If `float`, same spacing x and y spacing.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, a node may not be present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according certain their positions. Currently not used.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

FramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import FramedVoronoiGraph
>>> graph = FramedVoronoiGraph((3, 2))
>>> graph.number_of_nodes
6
```
__init__(shape, xy_spacing=(1.0, 1.0), xy_of_lower_left=(0.0, 0.0), sort=False, xy_min_spacing=(0.5, 0.5), seed=200)[source]#

Create the graph.

Parameters:
• shape (tuple of int) – Number of rows and columns of nodes.

• xy_spacing (float or tuple of float, optional) – Node spacing along x and y coordinates. If `float`, same spacing x and y spacing.

• xy_of_lower_left (tuple, optional) – Minimum x-of-node and y-of-node values. Depending on the grid, a node may not be present at this location.

• sort (bool) – If `True`, nodes, links and patches are re-numbered according certain their positions. Currently not used.

• xy_min_spacing (float or tuple of float, optional) – Final minimal spacing between nodes. Random moves of the core nodes around their position cannot be above this threshold: `(xy_spacing - xy_min_spacing) / 2` If `float`, same minimal spacing for x and y.

• seed (int, optional) – Seed used to generate the random x and y moves. When set, controls a pseudo-randomness of moves to ensure reproducibility. When `None`, seed is random and the moves of coordinates are completely random.

Returns:

A newly-created graph.

Return type:

FramedVoronoiGraph

Examples

Create a grid with 3 rows and 2 columns of nodes.

```>>> from landlab.graph import FramedVoronoiGraph
>>> graph = FramedVoronoiGraph((3, 2))
>>> graph.number_of_nodes
6
```
property node_layout#
property nodes_at_bottom_edge#
property nodes_at_left_edge#
property nodes_at_right_edge#
property nodes_at_top_edge#
property orientation#
property perimeter_nodes#

Get nodes on the convex hull of a Graph.

Examples

```>>> import numpy as np
>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> np.sort(graph.perimeter_nodes)
array([0, 2, 3, 5])
```
property shape#
property xy_spacing#