pcds (version 0.1.8)

IarcCSt1.std.tri: The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with \(t=1\)

Description

Returns \(I(\)p2 is in \(N_{CS}(p1,t=1))\) for points p1 and p2, that is, returns 1 if p2 is in \(N_{CS}(p1,t=1)\), returns 0 otherwise, where \(N_{CS}(x,t=1)\) is the CS proximity region for point \(x\) with expansion parameter \(t=1\).

CS proximity region is defined with respect to the standard equilateral triangle \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) and edge regions are based on the center of mass \(CM=(1/2,\sqrt{3}/6)\).

If p1 and p2 are distinct and either are outside \(T_e\), it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

Usage

IarcCSt1.std.tri(p1, p2)

Value

\(I(\)p2 is in \(N_{CS}(p1,t=1))\) for p1 in \(T_e\) 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

See Also

IarcCSstd.tri

Examples

# \donttest{
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
n<-3

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

IarcCSt1.std.tri(Xp[1,],Xp[2,])
IarcCSt1.std.tri(c(.2,.5),Xp[2,])
# }