Gam2CS.Te.onesixth: The indicator for two points constituting a dominating set for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one sixth of the standard equilateral triangle case

Description

Returns I({pt1,pt2} is a dominating set of the CS-PCD) where the vertices of the CS-PCD are the 2D data set Dt), that is, returns 1 if p is a dominating point of CS-PCD, returns 0 otherwise.

CS proximity region is constructed with respect to the standard equilateral triangle \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) and with expansion parameter \(t=1\). Point, pt1, must lie in the first one-sixth of \(T_e\), which is the triangle with vertices \(T(A,D_3,CM)=T((0,0),(1/2,0),CM)\).

ch.data.pnts is for checking whether points pt1 and pt2 are data points in Dt or not (default is FALSE), so by default this function checks whether the points pt1 and pt2 would be a dominating set if they actually were in the data set.

See also (ceyhan:Phd-thesis;textualpcds).

Usage

Gam2CS.Te.onesixth(pt1, pt2, Dt, ch.data.pnts = FALSE)

Arguments

pt1, pt2

Two 2D points to be tested for constituting a dominating set of the CS-PCD.

A set of 2D points which constitutes the vertices of the CS-PCD.

ch.data.pnts

A logical argument for checking whether points pt1 and pt2 are data points in Dt or not (default is FALSE).

Value

I({pt1,pt2} is a dominating set of the CS-PCD) where the vertices of the CS-PCD are the 2D data set Dt), that is, returns 1 if {pt1,pt2} is a dominating set of CS-PCD, returns 0 otherwise

References

Examples

Run this code

# NOT RUN {
n<-5

set.seed(1)
dat<-rbind(runifTe.onesixth(n)$gen.points,runifTe(n)$gen.points)

Gam2CS.Te.onesixth(dat[1,],dat[2,],dat)
Gam2CS.Te.onesixth(dat[1,],dat[3,],dat)
Gam2CS.Te.onesixth(c(.2,.2),dat[2,],dat)

Gam2CS.Te.onesixth(c(.2,.1),c(.3,.1),rbind(c(.2,.1),c(.3,.1)))
Gam2CS.Te.onesixth(c(1.2,1.1),c(1.3,1.1),rbind(c(1.2,1.1),c(1.3,1.1)))

n<-nrow(dat)
ind.gam2<-vector()
for (i in 1:(n-1))
 for (j in (i+1):n)
 {if (Gam2CS.Te.onesixth(dat[i,],dat[j,],dat)==1)
   ind.gam2<-rbind(ind.gam2,c(i,j))}

ind.gam2

P1<-c(.2,.1)
P2<-c(.3,.1)
Gam2CS.Te.onesixth(P1,c(.4,.2),dat)

dat.fr<-data.frame(a=dat)
Gam2CS.Te.onesixth(c(.4,.2),P2,dat.fr)

Gam2CS.Te.onesixth(c(.2,.2),dat[2,],dat,ch.data.pnts = TRUE)
#gives an error message since not both points are data points in Dt
# }
# NOT RUN {
# }