IndCSTet1: 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 \(I(\)pt2 is in \(N_{CS}(pt1,t=1))\) for points pt1 and pt2, that is, returns 1 if pt2 is in \(N_{CS}(pt1,t=1)\), 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 pt1 and pt2 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

IndCSTet1(pt1, pt2)

Value

\(I(\)pt2 is in \(N_{CS}(pt1,t=1))\) for pt1 in \(T_e\) that is, returns 1 if pt2

is in \(N_{CS}(pt1,t=1)\), returns 0 otherwise

Arguments

pt1: A 2D point whose CS proximity region is constructed.
pt2: A 2D point. The function determines whether pt2 is inside the CS proximity region of pt1 or not.

Author

Elvan Ceyhan

Examples

Run this code

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
n<-10

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

IndCSTet1(dat[1,],dat[2,])
IndCSTet1(dat[1,],dat[1,])

IndCSTet1(dat[2,],dat[5,])
IndCSTet1(c(.2,.5),dat[2,])

IndCSTet1(c(.2,.5),c(.2,.5))

IndCSTet1(dat[1,],dat[7,])