pcds (version 0.1.8)

rassoc.tri: Generation of points associated (in a Type I fashion) with the vertices of a triangle

Description

An object of class "Patterns". Generates n points uniformly in the support for Type I association in a given triangle, tri. delta is the parameter of association (that is, only \(\delta 100\) % area around each vertex in the triangle is allowed for point generation). delta corresponds to eps in the standard equilateral triangle \(T_e\) as \(delta=4eps^2/3\) (see rseg.std.tri function).

See (ceyhan:arc-density-PE,ceyhan:arc-density-CS,ceyhan:dom-num-NPE-Spat2011;textualpcds) for more on the association pattern.

Usage

rassoc.tri(n, tri, delta)

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

Attraction parameter, delta, of the Type I association pattern. delta is in \((0,1)\) and only \(\delta 100\) % of the area around vertices of the triangle tri is allowed for point generation.

ref.points

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

gen.points

The output set of generated points associated with the vertices of tri.

tri.Y

Logical output, TRUE if triangulation based on Yp points should be implemented.

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., Yp) points.

xlimit,ylimit

The ranges of the \(x\)- and \(y\)-coordinates of the reference points, which are the Yp points

Arguments

n

A positive integer representing the number of points to be generated from the association 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 association (that is, only \(\delta 100\) % area around vertices of the triangle is allowed for point generation).

Author

Elvan Ceyhan

References

See Also

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

Examples

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

Xdt<-rassoc.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 Association \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)
# }