Construct a penta-hexagonal icosahedral grid

The hexagrid function constrcucts a hexa-pentagonal grid based on the inversion of a tessellated icosahedron.

Arguments

tessellation: (numeric) An integer vector with the tessellation values. Each number describes the number of new edges replacing one original edge. Multiple series of tessellations are possible this way. The total tessellation is the product of the tessellation vector. Higher values result in more uniform cell sizes, but the larger number of tessellation series, increases the speed of lookup functions.
deg: (numeric) The target edge length of the grid in degrees. If provided, the function will select the appropriate tessellation vector from the hexguide-table, which is closest to the target. Note that these are unlikely to be the exact matches.
sp: (logical) Flag indicating whether the SpatialPolygons class representation of the grid should be added to the object when the grid is calculated. If set to true the SpPolygons function will be run with with the resolution parameter set to 25. The resulting object will be stored in slot @sp. As the calculation of this object can increase the grid creation time substantially by default this argument has a value FALSE. This can be added on demand by running the function newsp.
graph: (logical) Flag indicating whether the igraph class representation of the grid should be added to the object when the grid is calculated. This argument defaults to TRUE because this option has only minor performance load on the grid constructor function. For familiarization with the object structure, however, setting this parameter to FALSE might help, as invoking str on the 'igraph' class slot of the class might flood the console.
radius: (numeric) The radius of the grid. Defaults to the authalic radius of Earth.
center: (numeric) The origin of the grid in the reference Cartesian coordinate system. Defaults to c(0,0,0).
verbose: (logical) Should messages be printed during grid creation?

Value

A hexagonal grid object, with class hexagrid.

Details

Inherits from the trigrid class.

The grid structure functions as a frame for data graining, plotting and calculations. Data can be stored in layers that are linked to the grid object. In the current version only the facelayer class is implemented which allows the user to render data to the cells of the grid which are called faces. The grid 'user interface' is made up of four primary tables: the @vertices table for the coordinates of the vertices, the faceCenters for the coordinates of the centers of faces, the faces and the edges tables that contain which vertices form which faces and edges respectively. In these tables, the faces and vertices are sorted to form spirals that go from the north pole in a counter-clockwise direction. In case grid subsetting is performed these tables get truncated.

At finer resolutions, the large number of spatial elements render all calculations very resource demanding and slow, therefore the hierarchical structure created during the tessellation procedure is retained for efficient implementations. These data are stored in a list in the slot @skeleton and are 0-indexed integer tables for Rccp-based functions. $v stores vertex, $f the edge, and $e contains the edge data for plotting and calculations. In these tables the original hierarchy based orderings of the units are retained, during subsetting, additional vectors are used to indicate deactivation of these units. Any sort of meddling with the @skeleton object will lead to unexpected behavior.

Slots

vertices: Matrix of the vertex coordinates.
faces: Matrix of the verticies forming the faces
edges: Matrix of the vertices forming the edges.
tessellation: Contains the tessellation vector.
orientation: Contains the grid orientation in xyz 3d space, values in radian.
center: The xyz coordinates of the grid's origin/center.
div: Contains the number of faces that a single face of the previous tessellation level is decomposed to.
faceCenters: Contains the xyz coordinates of the centers of the faces on the surface of the sphere.

Examples

g <- hexagrid(c(8), sf=TRUE)
# based on approximate size (4 degrees edge length)
g1 <- hexagrid(deg=4) 
#> Selecting hexagrid with tessellation vector: c(2, 5).
#> Mean edge length: 3.995 degrees.