R: The closest points to circumcenter in each CC-vertex region...

cl2CCvert.reg.basic.tri {pcds}

R Documentation

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).

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

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.

Examples


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

[Package pcds version 0.1.8 Index]

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