rsegII.std.tri {pcds}

Generation of points segregated (in a Type II fashion) from the vertices of T_e

Description

An object of class "Patterns". Generates n points uniformly in the standard equilateral triangle T_e=T((0,0),(1,0),(1/2,\sqrt{3}/2)) under the type II segregation alternative for eps in (0,\sqrt{3}/6=0.2886751].

In the type II segregation, the annular forbidden regions around the edges are determined by the parameter eps which is the distance from the interior triangle (i.e., support for the segregation) to T_e (see examples for a sample plot.)

Usage

rsegII.std.tri(n, eps)

Arguments

n

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

eps

A positive real number representing the parameter of type II segregation (which is the distance from the interior triangle points to the boundary of T_e).

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

The exclusion parameter, eps, of the segregation pattern, which is the distance from the interior triangle to T_e

ref.points

The input set of points Y; reference points, i.e., points from which generated points are segregated (i.e., vertices of T_e).

gen.points

The output set of generated points segregated from Y points (i.e., vertices of T_e).

tri.Y

Logical output for triangulation based on Y points should be implemented or not. if TRUE triangulation based on Y 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 reference (i.e., Y) points, which is 3 here.

xlimit, ylimit

The ranges of the x- and y-coordinates of the reference points, which are the vertices of T_e here

Author(s)

Elvan Ceyhan

See Also

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

Examples

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
n<-10  #try also n<-20 or n<-100 or 1000
eps<-.15  #try also .2

set.seed(1)
Xdt<-rsegII.std.tri(n,eps)
Xdt
summary(Xdt)
plot(Xdt,asp=1)

Xlim<-range(Te[,1])
Ylim<-range(Te[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

Xp<-Xdt$gen.points

plot(Te,pch=".",xlab="",ylab="",
main="Type II segregation in the \n standard equilateral triangle",
     xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01))
polygon(Te)
points(Xp)

#The support for the Type II segregation alternative
C1<-c(1/2,sqrt(3)/2-2*eps);
A1<-c(eps*sqrt(3),eps); B1<-c(1-eps*sqrt(3),eps);
supp<-rbind(A1,B1,C1)

plot(Te,asp=1,pch=".",xlab="",ylab="",
main="Support of the Type II Segregation",
     xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01))
  polygon(Te)
  polygon(supp,col=5)
points(Xp)