spatstat.linnet (version 3.4-0)

lineardirichlet: Dirichlet Tessellation on a Linear Network

Description

Given a point pattern on a linear network, compute the Dirichlet (or Voronoi or Thiessen) tessellation induced by the points.

Usage

lineardirichlet(X, metric=c("shortestpath", "Euclidean"))

Value

A tessellation on a linear network (object of class "lintess").

Arguments

X

Point pattern on a linear network (object of class "lpp").

metric

Character string (partially matched) specifying the distance metric used to define the Dirichlet tessellation.

Missing tiles

If the linear network is not connected, and if one of the connected components contains no data points, then the Dirichlet tessellation using metric="shortestpath" is mathematically undefined inside this component. The resulting tessellation object includes a tile with label NA, which contains this component of the network. A plot of the tessellation will not show this tile.

Author

Adrian Baddeley .

Details

The Dirichlet tessellation induced by a point pattern X on a linear network L is a partition of L into subsets. The subset L[i] associated with the data point X[i] is the part of L lying closer to X[i] than to any other data point X[j].

If metric="shortestpath" (the default), distance between points on the network is measured by the shortest path in the network. If metric="Euclidean", distance is measured by the Euclidean distance in two dimensions.

See Also

lintess.

For the Dirichlet tessellation in two-dimensional space, see dirichlet.

Examples

  X <- runiflpp(5, simplenet)
  plot(lineardirichlet(X), lwd=3)
  points(X)
  plot(lineardirichlet(X, metric="E"), lwd=3)
  points(X)
  plot(dirichlet(as.ppp(X)), add=TRUE, lty=2)