spatgraphs (version 2.62)

spatgraphs-package: Graphs for spatial point patterns

Description

Compute various spatial graphs for 2D and 3D spatial point patterns such as the ppp-objects in R-package spatstat. Also capable of cluster/component computation and visualization.

Details

This package provides the following graph computations, all handled by the spatgraph-function:

Graph relation x~y ------------------------------------------------------------- Geometric ||x-y||

where ||.|| ~ Euclidian distance m(x) ~ mass, size i.e. real mark of x dn(x) ~ the distance to the nearest neighbour of x. knn(x) ~ the k nearest neighbours set of x The minimum spanning tree is computed using Prim's algorithm.

The classes sg and sgc are defined, with their own plot- and print-methods. 3D plotting requires package rgl.

For adjacency matrices see functions sg2adj and adj2sg.

In addition to the main workhorse spatgraph-function are the following functions: Function name Description ---------------------------------------------------------- spatcluster Compute clusters (connected components) shortestPath Find the shortest edge-path between two points edgeLengths Lenghts of edges in a graph sg2sym Make the edges symmetric sg2adj Convert to an adjacency matrix form cut.sg Cut edges longer than given R>0 prune.sg Prunes the graph, aimed for MST clip.sg Clip edges crossing the borders of a window. Useful for non-convex regions. sg2dxf Write a graph to a dxf file sg2igraph Change the sg-object to igraph-object of package \code{\link{igraph}} sg2sparse Convert between sg-object and Matrix-package sparseMatrix runif3d Simple 3d uniform pp generation spectral.sg Spectral clustering

References

Dousse, O., Baccelli, F. & Thiran, P.: Impact of Interferences on Connectivity in Ad Hoc Networks. IEEE/ACM Transactions on Networking,13 (2),p. 425-436,2005.

Marchette, D.: Random Graphs for Statistical Pattern Recognition, Wiley 2004.

See Also

Spatial point processes in general, see the package spatstat.

For more versatile Voronoi/Delaunay handling, see the package tripack or deldir.

The package rgl is required for 3D-plotting.

Examples

graph_example2d<-function(n=50,k=2,R=0.2)
  {
   pp2d<-list(x=runif(n),y=runif(n),n=n,window=list(x=c(0,1),y=c(0,1)))
   e1<-spatgraph(pp2d,"geometric",par=R)
   e2<-spatgraph(pp2d,"knn",par=k)
   e3<-spatgraph(pp2d,"MST")
   A<-spatcluster(e2)
   par(mfrow=c(1,3))
   plot(pp2d,main=paste("Geometric,R =",R))
   plot(e1,pp2d)
   plot(pp2d,main=paste("k-nn, k =",k))
   plot(e2,pp2d)
   plot(A,pp2d,pch=19)
   plot(pp2d, main="Minimum spanning tree")
   plot(e3,pp2d)
  }
  graph_example2d()

## 3d example, requires library rgl
  library(rgl)
  graph_example3d<-function(n=200)
  {
	w<-c(0,1)
	phi<-runif(n,0,pi);tau<-runif(n,0,2*pi);r<-runif(n)^0.33
	pp3d<-list(x=r*sin(tau)*cos(phi),y=r*cos(phi)*cos(tau),z=r*cos(phi),n=n,window=list(x=w,y=w,z=w))
	e<-spatgraph(pp3d,"RST",par=c(x=0,y=0,z=0))
	plot3d(pp3d,size=2, main="Radial spanning tree",col="black")
	plot(e,pp3d,col="plum")
  }
  graph_example3d()