pcds (version 0.1.1)

six.ext: The closest points among a data set in the standard equilateral triangle to the median lines in 6 half edge regions

Description

An object of class "Extrema". Returns the six closest points among the data set, Dt, in the standard equilateral triangle \(T_e=T(A=(0,0),B=(1,0),C=(1/2,\sqrt{3}/2))\) in half edge regions. In particular, in regions \(r_1\) and \(r_6\), it finds the closest point in each region to the line segment [A,CM] in regions \(r_2\) and \(r_3\), it finds the closest point in each region to the line segment [B,CM] and in regions \(r_4\) and \(r_5\), it finds the closest point in each region to the line segment [C,CM] where \(CM=(A+B+C)/3\) is the center of mass.

See the example for this function or example for rel.six.Te function. If there is no data point in region \(r_i\), then it returns "NA NA" for ith row in the extrema. ch.all.intri is for checking whether all data points are in \(T_e\) (default is FALSE).

Usage

six.ext(Dt, ch.all.intri = FALSE)

Arguments

Dt

A set of 2D points among which the closest points in the standard equilateral triangle to the median lines in 6 half edge regions.

ch.all.intri

A logical argument for checking whether all data points are in \(T_e\) (default is FALSE).

Value

A list with the elements

txt1

Region labels as r1-r6 (corresponds to row number in Extrema Points).

txt2

A short description of the distances as "Distances to Line Segments (A,CM), (B,CM), and (C,CM) in the six regions r1-r6".

type

Type of the extrema points

mtitle

The "main" title for the plot of the exrema

ext

The extrema points, here, closest points in each of regions r1-r6 to the line segments joining vertices to the center of mass, CM.

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 \(T_e\).

cent

The center point used for construction of edge regions.

ncent

Name of the center, cent, it is center of mass "CM" for this function.

regions

The six regions, r1-r6 and edge regions inside the triangle, \(T_e\), provided as a list.

region.names

Names of the regions as "r1"-"r6" and names of the edge regions as "er=1","er=2","er=3".

region.centers

Centers of mass of the regions r1-r6 and of edge regions inside \(T_e\).

dist2ref

Distances from closest points in each of regions r1-r6 to the line segments joining vertices to the center of mass, CM.

See Also

rel.six.Te and cl2edgesTe

Examples

# NOT RUN {
n<-10  #try also n<-100
dat<-runifTe(n)$gen.points

Ext<-six.ext(dat)
Ext
summary(Ext)
plot(Ext)

six.ext(dat[1:5,])$ext
sixt<-six.ext(dat)

A<-c(0,0); B<-c(1,0); C<-c(0.5,sqrt(3)/2);
Te<-rbind(A,B,C)
CM<-(A+B+C)/3
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

h1<-c(1/2,sqrt(3)/18); h2<-c(2/3, sqrt(3)/9); h3<-c(2/3, 2*sqrt(3)/9);
h4<-c(1/2, 5*sqrt(3)/18); h5<-c(1/3, 2*sqrt(3)/9); h6<-c(1/3, sqrt(3)/9);

r1<-(h1+h6+CM)/3;r2<-(h1+h2+CM)/3;r3<-(h2+h3+CM)/3;
r4<-(h3+h4+CM)/3;r5<-(h4+h5+CM)/3;r6<-(h5+h6+CM)/3;

Xlim<-range(Te[,1],dat[,1])
Ylim<-range(Te[,2],dat[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(A,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Te)
L<-Te; R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
polygon(rbind(h1,h2,h3,h4,h5,h6))
points(dat)
points(sixt$ext,pty=2,pch=4,col="red")

txt<-rbind(Te,r1,r2,r3,r4,r5,r6)
xc<-txt[,1]+c(-.02,.02,.02,0,0,0,0,0,0)
yc<-txt[,2]+c(.02,.02,.03,0,0,0,0,0,0)
txt.str<-c("A","B","C","1","2","3","4","5","6")
text(xc,yc,txt.str)

dat.fr<-data.frame(a=dat)
six.ext(dat.fr)

dat2<-rbind(dat,c(.8,.8))
six.ext(dat2)

six.ext(dat2,ch.all.intri = TRUE)
#gives an error message since not all data points are in the std equilateral triangle
# }
# NOT RUN {
# }