# ve {voronoi}

Voronoi intensity estimation
Package:
voronoi
Version:
1.1

### Description

Obtain the Voronoi intensity estimate for a point pattern.

### Usage

```ve(x, rw=NULL, locations=NULL)
```

### Arguments

x
An `M`-by-`2` matrix or data frame representing a point pattern, a `deldir` object, or a `ve` object.
rw
An optional vector of length 4 describing the corners of the rectangular space of the data. The values should be in the order of `(xmin, xmax, ymin, ymax)`. The default window is 20 percent larger than the range in each dimension -- 10 percent below and 10 percent above the minimum and maximum. This argument is only utilized when `x` is a matrix or data frame.
locations
A `N`-by-`2` matrix of locations to identify the Voronoi estimate.

### Details

The intensity estimate is the inverse-area of each Voronoi cell.

### Values

The output object is of class `""`, which itself is a list with the following items:

p
A matrix of the points.
z
A vector of the Voronoi estimates at the points.
T
A `deldir` object for the points.
rw
The rectangular space used for the data in the order of `(xmin, xmax, ymin, ymax)`.
est
A matrix with three columns, where the first two columns represent the argument `locations` and the third column is the Voronoi estimates at those locations.

### 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.

`centroidal`, `fd`

### Examples

```#=====> Equivalent Constructions <=====#
x <- rnorm(50, 1)
y <- rnorm(50, 6, 3)
d <- deldir(x, y)
t1 <- ve(cbind(x,y))
t2 <- ve(d)
identical(t1,t2)
par(mfrow=c(1,2))
plot(t1)
plot(t2)
points(t2)

#=====> Four Simulated Patterns <=====#
par(mfrow=c(2,2))

x  <- rnorm(100)
y  <- rnorm(100)
d1 <- deldir(x,y)
t3 <- ve(d1)
temp <- summary(t3)
plot(temp)

p    <- pattern.sim(6.5, type='linear')
t4   <- ve(p, rw=c(0,1,0,1))
st4  <- summary(t4)
plot(st4)

p  <- pattern.sim(6.5, type='moon')
t5 <- ve(p, rw=c(0,1,0,1))
plot(t5)
points(t5, cex=0.2)

p   <- pattern.sim(6.5, type='ridge')
t6  <- ve(p, rw=c(0,1,0,1))
plot(t6)
points(t6, cex=0.2)```

### Author(s)

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

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