Kfr2vVRCC: The `k` furthest points in a data set from vertices in each \(CC\)-vertex region in a triangle

Description

An object of class "Extrema". Returns the k furthest data points among the data set, Dt, in each \(CC\)-vertex region from the vertex in the triangle, tri\(=T(A,B,C)\), vertices are stacked row-wise. 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).

In the extrema, \(ext\), in the output, the first k entries are the k furthest points from vertex 1, second k entries are k furthest points are from vertex 2, and last k entries are the k furthest points from vertex 3. If data size does not allow, NA's are inserted for some or all of the k furthest points for each vertex.

Usage

Kfr2vVRCC(Dt, tri, k, ch.all.intri = FALSE)

Value

A list with the elements

txt1: Vertex labels are \(A=1\), \(B=2\), and \(C=3\) (corresponds to row number in Extremum Points).
txt2: A shorter description of the distances as "Distances of k furthest points in the vertex regions to Vertices".
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, k furthest points from vertices in each \(CC\)-vertex region in the triangle tri.
X: The input data, Dt, can be a matrix or data frame
num.points: The number of data points, i.e., size of Dt
supp: Support of the data points, it is tri for this function.
cent: The center point used for construction of vertex regions
ncent: Name of the center, cent, it is circumcenter "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 \(T_b\).
dist2ref: Distances from k furthest points in each vertex region to the corresponding vertex (each row representing a vertex in tri). Among the distances the first k entries are the distances from the k furthest points from vertex 1 to vertex 1, second k entries are distances from the k furthest points from vertex 2 to vertex 2, and the last k entries are the distances from the k furthest points from vertex 3 to vertex 3.

Arguments

Dt: A set of 2D points representing the set of data points.
tri: Three 2D points, stacked row-wise, each row representing a vertex of the triangle.
k: A positive integer. k furthest data points in each \(CC\)-vertex region are to be found if exists, else NA are provided for (some of) the k furthest points.
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.

Author

Elvan Ceyhan

Examples

Run this code

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10  #try also n<-20
k<-3

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

Ext<-Kfr2vVRCC(dat,Tr,k)
Ext
summary(Ext)
plot(Ext)

Kfr2vVRCC(dat[1:k,],Tr,k)
Kfr2vVRCC(dat[1,],Tr,k)

dat2<-rbind(dat,c(.2,.4))
Kfr2vVRCC(dat2,Tr,k)  #try also Kfr2vVRCC(dat2,Tr,k,ch.all.intri = TRUE)

kf2v<-Kfr2vVRCC(dat,Tr,k)

CC<-circ.cent.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],dat[,1])
Ylim<-range(Tr[,2],dat[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(A,pch=".",asp=1,xlab="",ylab="",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(dat)
points(kf2v$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,.04,.0,.02,.06,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)

Kfr2vVRCC(dat,Tr,k)

dat.fr<-data.frame(a=dat)
Kfr2vVRCC(dat.fr,Tr,k)

dat.fr<-data.frame(a=Tr)
fr2vVRCC(dat,dat.fr)