IcosohedronGrid: Icosahedral multi-resolution grids

In LatticeKrig: Multi-Resolution Kriging Based on Markov Random Fields

Description

Creates a multi-resolution grid based on subdividing triangles starting with faces of an icosahedron.

Usage

IcosahedronGrid(K)

IcosahedronFaces(K)

Arguments

K	Number of levels.

Details

Creates a nearly regular grid by taking the first level as the 12 points from a regular icosahedron. The subsequent levels generate a finer set of points by subdividing each triangular face into 4 new triangles. The three new mid points from the subdivision are added to the previous nodes to give the new level of resolution. The triangles tend to be roughly equilateral and so the nodes will tend to be roughly equally space but there is some variation in distances among nearest neighbors.

To depict the faces and nodes in a snazzy way use the rgl package and the following code

library( rgl)
# show level 3
Level<- 3
    SGrid <- IcosahedronFaces(4)
    Tri <- SGrid$Face[[Level]]
    L <- dim(Tri)[3]
    plot3d(rbind(c(0, 0, 0)), xlim = c(-1, 1), ylim = c(-1, 1), 
        zlim = c(-1, 1), axes = FALSE, xlab = "", ylab = "", 
        zlab = "", type = "p", box = TRUE)
    for (k in 1:L) {
        U <- Tri[, , k]
        rgl.triangles(U, col = "grey80")
    }
    plot3d(SGrid$nodes[[Level]], col = "green4", type = "s", 
        radius = 0.03, add = TRUE)

Value

IcosahedronGrid A list with K components each component is a three column matrix giving the direction cosines for each grid point.

IcosahedronFaces A list with components

MutiGrid

The same list returned by IcosahedronGrid.

Faces

A list with K-1 components. Each components are the faces at a given level represented as a three dimensional array (3X3XN with N the number of faces and a given level). The array indices are vertices of triangle, coordinates and faces within a resolution level. e.g. to extract the 10th face (out of 80) for the 2nd level:

look<- IcosahedronFaces(3)$Faces
triangle <- (look[[2]])[,,10]
print (triangle)
           [,1]       [,2]      [,3]
[1,] -0.5257311 -0.8506508  0.000000
[2,] -0.8090170 -0.5000000  0.309017
[3,] -0.8090170 -0.5000000 -0.309017
rowSums( triangle^2)
[1] 1 1 1

triangle will be the 10th face for the second level where the columns are the 3d coordinates of the direction cosines and the rows index the three vertices.

toSphere A two column matrix of the longitudes and latitudes when the points are projected onto a unit sphere.

Author(s)

Doug Nychka and Zachary Thomas

Examples

# second level in lon lat coordinates 
look<- IcosahedronGrid(3)
lonlat<- toSphere( look[[3]])
plot( lonlat, xlab="lon", ylab="lat")

LatticeKrig documentation built on Nov. 9, 2019, 5:07 p.m.