rseg.tri {pcds}

Generation of points segregated (in a Type I fashion) from the vertices of a triangle

Description

An object of class "Patterns". Generates n points uniformly in the support for Type I segregation in a given triangle, tri.

delta is the parameter of segregation (that is, \delta 100 % of the area around each vertex in the triangle is forbidden for point generation). delta corresponds to eps in the standard equilateral triangle T_e as delta=4 eps^2/3 (see rseg.std.tri function).

See (Ceyhan et al. (2006); Ceyhan et al. (2007); Ceyhan (2011)) for more on the segregation pattern.

Usage

rseg.tri(n, tri, delta)

Arguments

n

A positive integer representing the number of points to be generated from the segregation pattern in the triangle, tri.

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

delta

A positive real number in (0,1). delta is the parameter of segregation (that is, \delta 100 % area around vertices of each Delaunay triangle is forbidden for point generation).

Value

A list with the elements

type

The type of the pattern from which points are to be generated

mtitle

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

parameters

Exclusion parameter, delta, of the Type I segregation pattern. delta is in (0,1) and \delta 100 % area around vertices of the triangle tri is forbidden for point generation.

ref.points

The input set of points, i.e., vertices of tri; reference points, i.e., points from which generated points are segregated.

gen.points

The output set of generated points segregated from the vertices of tri.

tri.Y

Logical output, if TRUE the triangle tri is also plotted when the corresponding plot function from the Patterns object is called.

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., vertex of tri, which is 3 here).

xlimit, ylimit

The ranges of the x- and y-coordinates of the reference points, which are the vertices of the triangle tri

Author(s)

Elvan Ceyhan

References

Ceyhan E (2011). “Spatial Clustering Tests Based on Domination Number of a New Random Digraph Family.” Communications in Statistics - Theory and Methods, 40(8), 1363-1395.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

Ceyhan E, Priebe CE, Wierman JC (2006). “Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.” Computational Statistics & Data Analysis, 50(8), 1925-1964.

See Also

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

Examples

n<-100
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C)
del<-.4

Xdt<-rseg.tri(n,Tr,del)
Xdt
summary(Xdt)
plot(Xdt)

Xp<-Xdt$g
Xlim<-range(Tr[,1])
Ylim<-range(Tr[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Tr,pch=".",xlab="",ylab="",
main="Points from Type I Segregation \n in one Triangle",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(Xp)
xc<-Tr[,1]+c(-.02,.02,.02)
yc<-Tr[,2]+c(.02,.02,.03)
txt.str<-c("A","B","C")
text(xc,yc,txt.str)