IarcCSt1.std.tri: The indicator for the presence of an arc from a point to...

In pcds: Proximity Catch Digraphs and Their Applications

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)

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

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

Author(s)

Elvan Ceyhan

See Also

IarcCSstd.tri

Examples

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,])

pcds documentation built on May 29, 2024, 9:36 a.m.