funsCSt1EdgeRegs: Each function is for the presence of an arc from a point in one of the edge regions to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with \(t=1\)

Description

Three indicator functions: IndNCSTeRABt1, IndNCSTeRBCt1 and IndNCSTeRACt1.

The function IndNCSTeRABt1 returns \(I(\)p2 is in \(N_{CS}(p1,t=1)\) for p1 in \(RAB\) (edge region for edge \(AB\), i.e., edge 3) in the standard equilateral triangle \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\);

IndNCSTeRBCt1 returns \(I(\)p2 is in \(N_{CS}(p1,t=1)\) for p1 in \(RBC\) (edge region for edge \(BC\), i.e., edge 1) in \(T_e\); and

IndNCSTeRACt1 returns \(I(\)p2 is in \(N_{CS}(p1,t=1)\) for p1 in \(RAC\) (edge region for edge \(AC\), i.e., edge 2) in \(T_e\).

That is, each function returns 1 if p2 is in \(N_{CS}(p1,t=1)\), returns 0 otherwise, where \(N_{CS}(x,t)\) is the CS proximity region for point \(x\) with expansion parameter \(t=1\).

Usage

IndNCSTeRABt1(p1, p2)
IndNCSTeRBCt1(p1, p2)
IndNCSTeRACt1(p1, p2)

Value

Each function returns \(I(\)p2 is in \(N_{CS}(p1,t=1))\) for p1, that is, returns 1 if p2 is in \(N_{CS}(p1,t=1)\), returns 0 otherwise

Arguments

p1: A 2D point whose CS proximity region is constructed.
p2: A 2D point. The function determines whether p2 is inside the CS proximity region of p1 or not.

Author

Elvan Ceyhan

Examples

Run this code

if (FALSE) {
#Examples for IndNCSTeRABt1
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
CM<-(A+B+C)/3
T3<-rbind(A,B,CM);

set.seed(1)
Xp<-runif.std.tri(10)$gen.points

IndNCSTeRABt1(Xp[1,],Xp[2,])

IndNCSTeRABt1(c(.2,.5),Xp[2,])
}

if (FALSE) {
#Examples for IndNCSTeRBCt1
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
CM<-(A+B+C)/3
T1<-rbind(B,C,CM);

set.seed(1)
Xp<-runif.std.tri(3)$gen.points

IndNCSTeRBCt1(Xp[1,],Xp[2,])

IndNCSTeRBCt1(c(.2,.5),Xp[2,])
}

if (FALSE) {
#Examples for IndNCSTeRACt1
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
CM<-(A+B+C)/3
T2<-rbind(A,C,CM);

set.seed(1)
Xp<-runif.std.tri(3)$gen.points

IndNCSTeRACt1(Xp[1,],Xp[2,])
IndNCSTeRACt1(c(1,2),Xp[2,])
}