cl2CCvert.reg.basic.tri: The closest points to circumcenter in each CC-vertex region...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

The closest points to circumcenter in each CC-vertex region in a standard basic 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 standard basic triangle T_b = T(A=(0,0),B=(1,0),C=(c_1,c_2))=(vertex 1,vertex 2,vertex 3). ch.all.intri is for checking whether all data points are inside T_b (default is FALSE).

See also (\insertCiteceyhan:Phd-thesis,ceyhan:mcap2012;textualpcds).

Usage

cl2CCvert.reg.basic.tri(Xp, c1, c2, ch.all.intri = FALSE)

Arguments

Xp	A set of 2D points representing the set of data points.
c1, c2	Positive real numbers which constitute the vertex of the standard basic triangle. adjacent to the shorter edges; c_1 must be in [0,1/2], c_2>0 and (1-c_1)^2+c_2^2 \le 1
ch.all.intri	A logical argument for checking whether all data points are inside T_b (default is FALSE).

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 ...".
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 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 T_b.
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, T_b, 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 closest points in each vertex region to CC.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

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

Examples

## Not run: 
c1<-.4; c2<-.6;
A<-c(0,0); B<-c(1,0); C<-c(c1,c2);
Tb<-rbind(A,B,C)
n<-15

set.seed(1)
Xp<-runif.basic.tri(n,c1,c2)$g

Ext<-cl2CCvert.reg.basic.tri(Xp,c1,c2)
Ext
summary(Ext)
plot(Ext)

c2CC<-Ext

CC<-circumcenter.basic.tri(c1,c2)  #the circumcenter
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

Xlim<-range(Tb[,1],Xp[,1])
Ylim<-range(Tb[,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(Tb)
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(c2CC$ext,pch=4,col=2)

txt<-rbind(Tb,CC,Ds)
xc<-txt[,1]+c(-.03,.03,.02,.07,.06,-.05,.01)
yc<-txt[,2]+c(.02,.02,.03,-.01,.03,.03,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)

Xp2<-rbind(Xp,c(.2,.4))
cl2CCvert.reg.basic.tri(Xp2,c1,c2,ch.all.intri = FALSE)
#gives an error message if ch.all.intri = TRUE
#since not all points are in the standard basic triangle

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.