Given a point pattern on a linear network, compute the Dirichlet (or Voronoi or Thiessen) tessellation induced by the points.
Point pattern on a linear network (object of class
The Dirichlet tessellation induced by a point pattern
on a linear network
is a partition of
L into subsets. The subset
associated with the data point
X[i] is the part of
lying closer to
X[i] than to any other data point
where distance is measured by the shortest path.
A tessellation on a linear network
(object of class
If the linear network is not connected, and if one of the connected
components contains no data points, then the Dirichlet tessellation
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.
X <- runiflpp(5, simplenet) plot(lineardirichlet(X), lwd=3) points(X)
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