fr2vertsCCvert.reg {pcds}

The furthest points in a data set from vertices in each CC-vertex region in a triangle

Description

An object of class "Extrema". Returns the furthest data points among the data set, Xp, in each CC-vertex region from the vertex in the triangle, tri=T(A,B,C). Vertex region labels/numbers correspond to the row number of the vertex in tri. 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 edges among the data points inside tri (yields NA if there are no data points inside tri).

See also (Ceyhan (2005, 2012)).

Usage

fr2vertsCCvert.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 furthest points to ...".

type

Type of the extrema points

desc

A short description of the extrema points

mtitle

The "main" title for the plot of the extrema

ext

The extrema points, here, furthest points from vertices in each CC-vertex region in the triangle tri.

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 the triangle tri for this function.

cent

The center point used for construction of edge regions.

ncent

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

regions

CC-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 furthest points in each vertex region to the corresponding vertex

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

fr2vertsCCvert.reg.basic.tri, fr2edgesCMedge.reg.std.tri, kfr2vertsCCvert.reg.basic.tri and kfr2vertsCCvert.reg

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<-fr2vertsCCvert.reg(Xp,Tr)
Ext
summary(Ext)
plot(Ext)

f2v<-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(Tr,xlab="",asp=1,ylab="",pch=".",
main="Furthest Points in CC-Vertex Regions \n from the Vertices",
axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(Xp)
points(rbind(f2v$ext),pch=4,col=2)

txt<-rbind(Tr,CC,Ds)
xc<-txt[,1]+c(-.06,.08,.05,.12,-.1,-.1,-.09)
yc<-txt[,2]+c(.02,-.02,.05,.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))
fr2vertsCCvert.reg(Xp2,Tr,ch.all.intri = FALSE)
#gives an error message if ch.all.intri = TRUE
#since not all points in the data set are in the triangle