pcds (version 0.1.1)

IndCS.Te.onesixth: The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one sixth of the standard equilateral triangle case

Description

Returns I(pt2 is in \(NCS(pt1,t=1)\)) for points pt1 and pt2, that is, returns 1 if pt2 is in \(NCS(pt1,t=1)\), returns 0 otherwise, where \(NCS(x,t=1)\) 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 \(CM=(1/2,\sqrt{3}/6)\). Here pt1 must lie in the first one-sixth of \(T_e\), which is the triangle with vertices \(T(A,D_3,CM)=T((0,0),(1/2,0),CM)\). If pt1 and pt2 are distint and pt1 is outside of \(T(A,D_3,CM)\) or pt2 is 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

IndCS.Te.onesixth(pt1, pt2)

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.

Value

I(pt2 is in \(NCS(pt1,t=1)\)) for pt1 in the first one-sixth of \(T_e\), \(T(A,D_3,CM)\), that is, returns 1 if pt2 is in \(NCS(pt1,t=1)\), returns 0 otherwise

See Also

IndCSTe

Examples

# NOT RUN {
n<-5

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

IndCS.Te.onesixth(dat[1,],dat[2,])
IndCS.Te.onesixth(dat[1,],dat[1,])
IndCS.Te.onesixth(dat[1,],dat[9,])
IndCS.Te.onesixth(c(.2,.5),dat[2,])
IndCS.Te.onesixth(c(.2,.5),c(.2,.5))

set.seed(1)
dat<-runifTe(10)$gen.points

IndCS.Te.onesixth(dat[1,],dat[2,])
# }
# NOT RUN {
# }