pcds (version 0.1.2)

IndNPETeSet: The indicator for the presence of an arc from a point in set S to the point pt for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

Description

Returns \(I(\)pt in \(N_{PE}(x,r)\) for some \(x\) in S\()\), that is, returns 1 if pt is in \(\cup_{x in S}N_{PE}(x,r)\), returns 0 otherwise.

PE proximity region is constructed with respect to the standard equilateral triangle \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) with the expansion parameter \(r \ge 1\) and vertex regions are based on center \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of \(T_e\); default is \(M=(1,1,1)\) i.e., the center of mass of \(T_e\) (which is equivalent to the circumcenter for \(T_e\)).

Vertices of \(T_e\) are also labeled as 1, 2, and 3, respectively. If pt is not in S and either pt or all points in S are outside \(T_e\), it returns 0, but if pt is in S, then it always returns 1 regardless of its location (i.e., loops are allowed).

Usage

IndNPETeSet(S, pt, r, M = c(1, 1, 1))

Arguments

S

A set of 2D points. Presence of an arc from a point in S to point pt is checked by the function.

pt

A 2D point. Presence of an arc from a point in S to point pt is checked by the function.

r

A positive real number which serves as the expansion parameter in PE proximity region in the standard equilateral triangle \(T_e=T((0,0),(1,0),(1/2,\sqrt{3}/2))\); must be \(\ge 1\).

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the standard equilateral triangle \(T_e\); default is \(M=(1,1,1)\) i.e., the center of mass of \(T_e\).

Value

I(pt is in U_x in S N_PE(x,r)), that is, returns 1 if pt is in S or inside \(N_{PE}(x,r)\) for at least one \(x\) in S, returns 0 otherwise. PE proximity region is constructed with respect to the standard equilateral triangle \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) with M-vertex regions

See Also

IndNPEtriSet, IndNPETe, IndNPEtri, and IndCSTeSet

Examples

# NOT RUN {
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

M<-as.numeric(runifTe(1)$g)  #try also M<-c(.6,.2)

r<-1.5

S<-rbind(dat[1,],dat[2,])  #try also S<-c(.5,.5)
IndNPETeSet(S,dat[3,],r,M)
IndNPETeSet(S,dat[3,],r=1,M)
IndNPETeSet(S,dat[3,],r=1.5,M)

S<-rbind(dat[1,],dat[2,],dat[3,],dat[5,])
IndNPETeSet(S,dat[3,],r,M)

IndNPETeSet(S,dat[6,],r,M)
IndNPETeSet(S,dat[6,],r=1.25,M)

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
IndNPETeSet(S,dat[3,],r,M)

IndNPETeSet(c(.2,.5),dat[2,],r,M)
IndNPETeSet(dat,c(.2,.5),r,M)
IndNPETeSet(dat,dat[2,],r,M)
IndNPETeSet(c(.2,.5),c(.2,.5),r,M)
IndNPETeSet(dat[5,],dat[2,],r,M)

S<-rbind(dat[1,],dat[2,],dat[3,],dat[5,],c(.2,.5))
IndNPETeSet(S,dat[3,],r,M)

P<-c(.4,.2)
S<-dat[c(1,3,4),]
IndNPETeSet(dat,P,r,M)

IndNPETeSet(rbind(S,S),P,r,M)

dat.fr<-data.frame(a=S)
IndNPETeSet(dat.fr,P,r,M)

# }