six.extremaTe {pcds}

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

Description

An object of class "Extrema". Returns the six closest points among the data set, Xp, 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 index.six.Te function. If there is no data point in region r_i, then it returns "NA NA" for i-th row in the extrema. ch.all.intri is for checking whether all data points are in T_e (default is FALSE).

Usage

six.extremaTe(Xp, ch.all.intri = FALSE)

Arguments

Xp

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 (correspond to row number in Extremum 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 extrema

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, 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_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", and "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.

Author(s)

Elvan Ceyhan

See Also

index.six.Te and cl2edges.std.tri

Examples

n<-20  #try also n<-100
Xp<-runif.std.tri(n)$gen.points

Ext<-six.extremaTe(Xp)
Ext
summary(Ext)
plot(Ext)

sixt<-Ext

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],Xp[,1])
Ylim<-range(Te[,2],Xp[,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(Xp)
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)