rassoc.circular {pcds}

Generation of points associated (in a radial or circular fashion) with a given set of points

Description

An object of class "Patterns". Generates n 2D points uniformly in (a_1-e,a_1+e) \times (a_1-e,a_1+e) \cap U_i B(y_i,e) (a_1 and b1 are denoted as a1 and b1 as arguments) where Y_p=(y_1,y_2,\ldots,y_{n_y}) with n_y being number of Yp points for various values of e under the association pattern and B(y_i,e) is the ball centered at y_i with radius e.

e must be positive and very large values of e provide patterns close to CSR. a1 is defaulted to the minimum of the x-coordinates of the Yp points, a2 is defaulted to the maximum of the x-coordinates of the Yp points, b1 is defaulted to the minimum of the y-coordinates of the Yp points, b2 is defaulted to the maximum of the y-coordinates of the Yp points. This function is also very similar to rassoc.matern, where rassoc.circular needs the study window to be specified, while rassoc.matern does not.

Usage

rassoc.circular(
  n,
  Yp,
  e,
  a1 = min(Yp[, 1]),
  a2 = max(Yp[, 1]),
  b1 = min(Yp[, 2]),
  b2 = max(Yp[, 2])
)

Arguments

n

A positive integer representing the number of points to be generated.

Yp

A set of 2D points representing the reference points. The generated points are associated (in a circular or radial fashion) with these points.

e

A positive real number representing the radius of the balls centered at Yp points. Only these balls are allowed for the generated points (i.e., generated points would be in the union of these balls).

a1, a2

Real numbers representing the range of x-coordinates in the region (default is the range of x-coordinates of the Yp points).

b1, b2

Real numbers representing the range of y-coordinates in the region (default is the range of y-coordinates of the Yp points).

Value

A list with the elements

type

The type of the point pattern

mtitle

The "main" title for the plot of the point pattern

parameters

Radial attraction parameter of the association pattern

ref.points

The input set of attraction points Yp, i.e., points with which generated points are associated.

gen.points

The output set of generated points associated with Yp points

tri.Yp

Logical output for triangulation based on Yp points should be implemented or not. if TRUE triangulation based on Yp points is to be implemented (default is set to FALSE).

desc.pat

Description of the point pattern

num.points

The vector of two numbers, which are the number of generated points and the number of attraction (i.e., Yp) points.

xlimit, ylimit

The possible range of the x- and y-coordinates of the generated points.

Author(s)

Elvan Ceyhan

See Also

rseg.circular, rassoc.std.tri, rassocII.std.tri, rassoc.matern, and rassoc.multi.tri

Examples

nx<-100; ny<-4;  #try also nx<-1000; ny<-10;

e<-.15;
#with default bounding box (i.e., unit square)
Y<-cbind(runif(ny),runif(ny))

Xdt<-rassoc.circular(nx,Y,e)
Xdt
summary(Xdt)
plot(Xdt,asp=1)

Xdt<-Xdt$gen.points
Xlim<-range(Xdt[,1],Y[,1]);
Ylim<-range(Xdt[,2],Y[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Y,asp=1,xlab="x",ylab="y",
main="Circular Association of X points with Y Points",
     xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01),
     pch=16,col=2,lwd=2)
points(Xdt)

#with default bounding box (i.e., unit square)
Xlim<-range(Xdt[,1],Y[,1]);
Ylim<-range(Xdt[,2],Y[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Y,asp=1,xlab="x",ylab="y",
main="Circular Association of X points with Y Points",
     xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01),pch=16,
     col=2,lwd=2)
points(Xdt)

#with a rectangular bounding box
a1<-0; a2<-10;
b1<-0; b2<-5;
e<-1.1;  #try also e<-5; #pattern very close to CSR!

Y<-cbind(runif(ny,a1,a2),runif(ny,b1,b2))
#try also Y<-cbind(runif(ny,a1,a2/2),runif(ny,b1,b2/2))

Xdt<-rassoc.circular(nx,Y,e,a1,a2,b1,b2)$gen.points
Xlim<-range(Xdt[,1],Y[,1]);
Ylim<-range(Xdt[,2],Y[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Y,asp=1,xlab="x",ylab="y",
main="Circular Association of X points with Y Points",
     xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01),
     pch=16,col=2,lwd=2)
points(Xdt)