cl2CCvert.reg {pcds}

The closest points to circumcenter in each CC-vertex region in a triangle

Description

An object of class "Extrema". Returns the closest data points among the data set, Xp, to circumcenter, CC, in each CC-vertex region in the triangle tri =T(A,B,C)=(vertex 1,vertex 2,vertex 3).

ch.all.intri is for checking whether all data points are inside tri (default is FALSE). If some of the data points are not inside tri and ch.all.intri=TRUE, then the function yields an error message. If some of the data points are not inside tri and ch.all.intri=FALSE, then the function yields the closest points to CC among the data points in each CC-vertex region of tri (yields NA if there are no data points inside tri).

See also (Ceyhan (2005, 2012)).

Usage

cl2CCvert.reg(Xp, tri, ch.all.intri = FALSE)

Arguments

Xp

A set of 2D points representing the set of data points.

tri

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

ch.all.intri

A logical argument (default=FALSE) to check whether all data points are inside the triangle tri. So, if it is TRUE, the function checks if all data points are inside the closure of the triangle (i.e., interior and boundary combined) else it does not.

Value

A list with the elements

txt1

Vertex labels are A=1, B=2, and C=3 (correspond to row number in Extremum Points).

txt2

A short description of the distances as "Distances from closest points to CC ..."

type

Type of the extrema points

mtitle

The "main" title for the plot of the extrema

ext

The extrema points, here, closest points to CC in each CC-vertex region

X

The input data, Xp, can be a matrix or data frame

num.points

The number of data points, i.e., size of Xp

supp

Support of the data points, here, it is tri

cent

The center point used for construction of vertex regions

ncent

Name of the center, cent, it is "CC" for this function

regions

Vertex regions inside the triangle, tri, provided as a list

region.names

Names of the vertex regions as "vr=1", "vr=2", and "vr=3"

region.centers

Centers of mass of the vertex regions inside tri

dist2ref

Distances from closest points in each CC-vertex region to CC.

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.

See Also

cl2CCvert.reg.basic.tri, cl2edges.vert.reg.basic.tri, cl2edgesMvert.reg, cl2edgesCMvert.reg, and fr2edgesCMedge.reg.std.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10  #try also n<-20

set.seed(1)
Xp<-runif.tri(n,Tr)$g

Ext<-cl2CCvert.reg(Xp,Tr)
Ext
summary(Ext)
plot(Ext)

c2CC<-Ext

CC<-circumcenter.tri(Tr)  #the circumcenter
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

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

plot(A,pch=".",asp=1,xlab="",ylab="",
main="Closest Points in CC-Vertex Regions \n to the Circumcenter",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(Xp)
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(c2CC$ext,pch=4,col=2)

txt<-rbind(Tr,CC,Ds)
xc<-txt[,1]+c(-.07,.08,.06,.12,-.1,-.1,-.09)
yc<-txt[,2]+c(.02,-.02,.03,.0,.02,.06,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)

Xp2<-rbind(Xp,c(.2,.4))
cl2CCvert.reg(Xp2,Tr,ch.all.intri = FALSE)
#gives an error message if ch.all.intri = TRUE since not all points are in the triangle