kfr2vertsCCvert.reg.basic.tri {pcds} | R Documentation |
The k
furthest points from vertices
in each CC
-vertex region in a standard basic triangle
Description
An object of class "Extrema"
.
Returns the k
furthest data points
among the data set, Xp
,
in each CC
-vertex region from the vertex in the
standard basic triangle T_b=T(A=(0,0),B=(1,0),C=(c_1,c_2))
.
Any given triangle can be mapped to the standard basic triangle by a combination of rigid body motions (i.e., translation, rotation and reflection) and scaling, preserving uniformity of the points in the original triangle. Hence, standard basic triangle is useful for simulation studies under the uniformity hypothesis.
ch.all.intri
is for checking whether all data points are
inside T_b
(default is FALSE
).
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
kfr2vertsCCvert.reg.basic.tri(Xp, c1, c2, k, 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;
|
k |
A positive integer. |
ch.all.intri |
A logical argument for checking
whether all data points are inside |
Value
A list
with the elements
txt1 |
Vertex labels are |
txt2 |
A shorter description of the distances
as |
type |
Type of the extrema points |
desc |
A short description of the extrema points |
mtitle |
The |
ext |
The extrema points, here,
|
X |
The input data, |
num.points |
The number of data points, i.e., size of |
supp |
Support of the data points,
here, it is |
cent |
The center point used for construction of edge regions. |
ncent |
Name of the center, |
regions |
Vertex regions inside the triangle, |
region.names |
Names of the vertex regions
as |
region.centers |
Centers of mass of the vertex regions inside |
dist2ref |
Distances from |
Author(s)
Elvan Ceyhan
See Also
fr2vertsCCvert.reg.basic.tri
, fr2vertsCCvert.reg
,
fr2edgesCMedge.reg.std.tri
, and kfr2vertsCCvert.reg
Examples
c1<-.4; c2<-.6;
A<-c(0,0); B<-c(1,0); C<-c(c1,c2);
Tb<-rbind(A,B,C)
n<-20
k<-3
set.seed(1)
Xp<-runif.basic.tri(n,c1,c2)$g
Ext<-kfr2vertsCCvert.reg.basic.tri(Xp,c1,c2,k)
Ext
summary(Ext)
plot(Ext)
kf2v<-Ext
CC<-circumcenter.basic.tri(c1,c2) #the circumcenter
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)
Xlim<-range(Tb[,1],Xp[,1])
Ylim<-range(Tb[,2],Xp[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
plot(A,pch=".",asp=1,xlab="",ylab="",
main=paste(k," Furthest Points in CC-Vertex Regions \n from the Vertices",sep=""),
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tb)
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(Xp)
points(kf2v$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,-.02,.02,.03,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)