funsCSt1EdgeRegs {pcds}

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: IarcCSt1.std.triRAB, IarcCSt1.std.triRBC and IarcCSt1.std.triRAC.

The function IarcCSt1.std.triRAB 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));

IarcCSt1.std.triRBC 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

IarcCSt1.std.triRAC 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

IarcCSt1.std.triRAB(p1, p2)

IarcCSt1.std.triRBC(p1, p2)

IarcCSt1.std.triRAC(p1, p2)

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.

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

Author(s)

Elvan Ceyhan

See Also

IarcCSstd.triRAB, IarcCSstd.triRBC and IarcCSstd.triRAC

Examples

#Examples for IarcCSt1.std.triRAB
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

IarcCSt1.std.triRAB(Xp[1,],Xp[2,])

IarcCSt1.std.triRAB(c(.2,.5),Xp[2,])



#Examples for IarcCSt1.std.triRBC
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

IarcCSt1.std.triRBC(Xp[1,],Xp[2,])

IarcCSt1.std.triRBC(c(.2,.5),Xp[2,])



#Examples for IarcCSt1.std.triRAC
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

IarcCSt1.std.triRAC(Xp[1,],Xp[2,])
IarcCSt1.std.triRAC(c(1,2),Xp[2,])