# voronoi-package {voronoi}

Methods and applications related to Voronoi tessellations
Package:
voronoi
Version:
1.1

### Description

Methods and applications related to Voronoi tessellations

### Details

 Package: voronoi Type: Package Version: 1.1 Date: 2011-08-08 License: GPL-3 Depends: R (>= 2.11.1), deldir, spatialkernel, splancs, gpclib LazyLoad: yes

### References

C.D Barr and F.P Schoenberg. On the Voronoi Estimator for the Intensity of an Inhomogeneous Planar Poisson Process. Biometrika, 1:1-15, 2010.

Q. Du, V. Faber and M. Gunzburger. Centroidal Voronoi Tesselations: Applications and Algorithms. SIAM Review 41:637-676, 1999.

C.G. Wager, B.A. Coull and N. Lange. Modelling Spatial Intensity for Replicated Inhomogeneous Point Patterns in Brain Imaging. J.R. Statist. Soc. B, 66:429-446, 2004.

`ve`, `centroidal`, `pattern.sim`, `voronoi.game`

### Examples

```#=====> ve <=====#
p  <- pattern.sim(7, type='moon')
t5 <- ve(p, rw=c(0,1,0,1))
plot(t5)
points(t5, cex=0.2)

#=====> centroidal <=====#
f           <- function(x, y) x^4 + y^4
antideriv.x <- function(x, y) x^5/5 + x*y^4
antideriv.y <- function(x, y) y*x^4 + y^5/5
obj         <- deldir(runif(10), runif(10))
c.obj       <- centroidal(x = obj, eps = .005, f = f,
antideriv.x = antideriv.x,
antideriv.y = antideriv.y,
divisions = 10, verbose = 5)
par(mfrow=c(1,2))
plot(obj, wlines="tess", main="Original Tessellation")
plot(c.obj\$T, wlines="tess", main="Centroidal Tessellation")

#=====> pattern.sim <=====#
par(mfrow = c(2,2))
plot(pattern.sim(type = "linear"), main = "linear")
plot(pattern.sim(type = "moon"), main = "moon")
plot(pattern.sim(type = "ridge"), main = "ridge")

for(i in 1:4) {
plot(pattern.sim(i + 6, type = "moon"),
main = paste("r = ", i + 6), pch = 20, cex = 0.2)
}

for(i in 1:4) {
plot(pattern.sim(i + 6, type = "ridge"),
main = paste("r = ", i + 6), pch = 20, cex = 0.2)
}```

### Author(s)

Christopher D. Barr, Travis A. Gerke, David M. Diez

Maintainer: Christopher D. Barr

Documentation reproduced from package voronoi, version 1.1. License: GPL-3