landlab.graph.quasi_spherical.dual_icosphere

icosphere_global_grid: Create a Landlab global (i.e., quasi-spherical) grid based on an IcoSphere, which is formed by iteratively densifying an icosahedron.

Greg Tucker, University of Colorado Boulder, September 2023

class DualIcosphereGraph[source]

Bases: object

A Landlab global (quasi-spherical) graph type based on an IcoSphere.

Parameters:

  • radius (float, optional) – Radius for the icosphere, m (default 1)

  • mesh_densification_level (int, optional) – Number of iterative subdivisions of initial triangles (default 0)

Initialize DualIcosphereGraph

Parameters:

  • radius (float, optional) – Radius of the sphere (default 1.0)

  • mesh_densification_level (int, optional) – Number of times to subdivide the mesh (default 0)

Notes

Data structures set up include the following (note that n_cells = n_nodes and n_faces = n_links): - coords_of_node : ndarray of float (n_nodes, 3) - x_of_node, y_of_node, z_of_node : ((n_nodes, ) views of coords_of_node) - coords_of_corner : ndarray of float (n_corners, 3) - x_of_corner, y_of_corner, z_of_corner : ndarray of float (n_corners, ) - length_of_link : ndarray of float (n_links, ) - nodes_at_link : ndarray of int (n_links, 2) - node_at_link_tail, node_at_link_head : (n_links, ) views of nodes_at_link - links_at_node : ndarray of int (n_nodes, 6) - cell_at_node, node_at_cell : ndarray of int (n_nodes, ) - corners_at_face : ndarray of int (n_links, 2) - corners_at_node, corners_at_cell : ndarray of int (n_nodes, 6) - area_of_cell : ndarray of float (n_nodes, ) - length_of_face : ndarray of float (n_links, ) - link_at_face, face_at_link : ndarray of int (n_links, ) - faces_at_cell : ndarray of int (n_nodes, 6) - adjacent_nodes_at_node : ndarray of int (n_nodes, 6)

Examples

>>> import numpy as np

Basic example: dodecahedron

>>> ico = DualIcosphereGraph()
>>> np.round(ico.coords_of_node[0], 3)
array([-0.526,  0.851,  0.   ])
>>> ico.r_of_node[0]
1.0
>>> int(ico.phi_of_node[0] * 100), int(ico.theta_of_node[0] * 100)
(212, 157)
>>> np.round(ico.coords_of_corner[1], 3)
array([-0.   ,  0.934,  0.357])
>>> round(ico.length_of_link[0], 3)
1.107
>>> ico.nodes_at_link[0]
array([ 0, 11])
>>> ico.links_at_node[0]
array([ 0,  2,  4,  6,  8, -1])
>>> ico.cell_at_node[0]
0
>>> ico.node_at_cell[1]
1
>>> ico.corners_at_face[0]
array([0, 4])
>>> int(10000 * ico.length_of_face[0])
7297
>>> ico.corners_at_node[0]
array([ 3,  4,  0,  1,  2, -1])
>>> ico.corners_at_cell[0]
array([ 3,  4,  0,  1,  2, -1])
>>> int(1e6 * ico.area_of_cell[0])
1047197
>>> ico.link_at_face[2]
2
>>> ico.face_at_link[3]
3
>>> ico.faces_at_cell[0]
array([ 0,  2,  4,  6,  8, -1])
>>> ico.adjacent_nodes_at_node[0]
array([11,  5,  1,  7, 10, -1])

Icosphere with 1 level of subdivision

>>> ico = DualIcosphereGraph(mesh_densification_level=1)
>>> ico.number_of_patches
80
__init__(radius=1.0, mesh_densification_level=0)[source]

Initialize DualIcosphereGraph

Parameters:

  • radius (float, optional) – Radius of the sphere (default 1.0)

  • mesh_densification_level (int, optional) – Number of times to subdivide the mesh (default 0)

Notes

Data structures set up include the following (note that n_cells = n_nodes and n_faces = n_links): - coords_of_node : ndarray of float (n_nodes, 3) - x_of_node, y_of_node, z_of_node : ((n_nodes, ) views of coords_of_node) - coords_of_corner : ndarray of float (n_corners, 3) - x_of_corner, y_of_corner, z_of_corner : ndarray of float (n_corners, ) - length_of_link : ndarray of float (n_links, ) - nodes_at_link : ndarray of int (n_links, 2) - node_at_link_tail, node_at_link_head : (n_links, ) views of nodes_at_link - links_at_node : ndarray of int (n_nodes, 6) - cell_at_node, node_at_cell : ndarray of int (n_nodes, ) - corners_at_face : ndarray of int (n_links, 2) - corners_at_node, corners_at_cell : ndarray of int (n_nodes, 6) - area_of_cell : ndarray of float (n_nodes, ) - length_of_face : ndarray of float (n_links, ) - link_at_face, face_at_link : ndarray of int (n_links, ) - faces_at_cell : ndarray of int (n_nodes, 6) - adjacent_nodes_at_node : ndarray of int (n_nodes, 6)

Examples

>>> import numpy as np

Basic example: dodecahedron

>>> ico = DualIcosphereGraph()
>>> np.round(ico.coords_of_node[0], 3)
array([-0.526,  0.851,  0.   ])
>>> ico.r_of_node[0]
1.0
>>> int(ico.phi_of_node[0] * 100), int(ico.theta_of_node[0] * 100)
(212, 157)
>>> np.round(ico.coords_of_corner[1], 3)
array([-0.   ,  0.934,  0.357])
>>> round(ico.length_of_link[0], 3)
1.107
>>> ico.nodes_at_link[0]
array([ 0, 11])
>>> ico.links_at_node[0]
array([ 0,  2,  4,  6,  8, -1])
>>> ico.cell_at_node[0]
0
>>> ico.node_at_cell[1]
1
>>> ico.corners_at_face[0]
array([0, 4])
>>> int(10000 * ico.length_of_face[0])
7297
>>> ico.corners_at_node[0]
array([ 3,  4,  0,  1,  2, -1])
>>> ico.corners_at_cell[0]
array([ 3,  4,  0,  1,  2, -1])
>>> int(1e6 * ico.area_of_cell[0])
1047197
>>> ico.link_at_face[2]
2
>>> ico.face_at_link[3]
3
>>> ico.faces_at_cell[0]
array([ 0,  2,  4,  6,  8, -1])
>>> ico.adjacent_nodes_at_node[0]
array([11,  5,  1,  7, 10, -1])

Icosphere with 1 level of subdivision

>>> ico = DualIcosphereGraph(mesh_densification_level=1)
>>> ico.number_of_patches
80
__new__(**kwargs)
property area_of_patch
property cell_at_node
property corners_at_cell
property faces_at_cell

Face-cell and node-link numbering are the same!

property node_at_cell
property patches_at_node
property phi_of_node
property r_of_node
property theta_of_node