fr2vVRCC: The furthest points in a data set from vertices in each $C C$ -vertex region in a triangle

Description

An object of class "Extrema". Returns the furthest data points among the data set, Dt, in each $C C$ -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:Phd-thesis,ceyhan:mcap2012;textualpcds).

Usage

fr2vVRCC(Dt, tri, 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 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 $C C$ -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, 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

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.
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

References

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

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

Ext<-fr2vVRCC(dat,Tr)
Ext
summary(Ext)
plot(Ext)

fr2vVRCC(dat[1,],Tr)
f2v<-fr2vVRCC(dat,Tr)

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(Tr,xlab="",asp=1,ylab="",pch=".",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(dat)
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)

fr2vVRCC(dat,Tr)

fr2vVRCC(c(1.4,1.2),Tr)

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

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

dat2<-rbind(dat,c(.2,.4))
fr2vVRCC(dat2,Tr)

fr2vVRCC(dat2,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

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