Vertices and Edges of Dirichlet Tessellation
Computes the Dirichlet-Voronoi tessellation of a point pattern and extracts the vertices or edges of the tiles.
dirichletVertices(X) dirichletEdges(X, clip=TRUE)
X |
Point pattern (object of class |
clip |
Logical value specifying whether to clip the tile edges to the window. See Details. |
These function compute the Dirichlet-Voronoi tessellation of X
(see dirichlet)
and extract the vertices or edges of the tiles of the tessellation.
The Dirichlet vertices are the spatial locations which are locally
farthest away from X, that is, where the distance function
of X reaches a local maximum.
The Dirichlet edges are the dividing lines equally distant between
a pair of points of X.
The Dirichlet tessellation of X is computed
using dirichlet. The vertices or edges of all
tiles of the tessellation are extracted.
For dirichletVertices, any vertex which
lies on the boundary of the window of X is deleted.
The remaining vertices are returned, as a point pattern,
without duplicated entries.
For dirichletEdges, the edges are initially computed
inside the rectangle Frame(X).
Then if clip=TRUE (the default), these edges are intersected
with Window(X), which may cause an edge to be broken into
several pieces.
dirichletVertices
returns a point pattern (object of class "ppp") in the same window
as X.
dirichletEdges returns a line segment pattern (object of
class "psp").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
plot(dirichlet(cells)) plot(dirichletVertices(cells), add=TRUE) ed <- dirichletEdges(cells)
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