pcds (version 0.1.4)

IndNCStriSet: The indicator for the presence of an arc from a point in set S to the point pt for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

Description

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

CS proximity region is constructed with respect to the triangle tri with the expansion parameter \(t>0\) and edge regions are based on the center, \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of the triangle tri; default is \(M=(1,1,1)\) i.e., the center of mass of tri.

Edges of tri\(=T(A,B,C)\), \(AB\), \(BC\), \(AC\), are also labeled as edges 3, 1, and 2, respectively. If pt is not in S and either pt or all points in S are outside tri, it returns 0, but if pt is in S, then it always returns 1 regardless of its location (i.e., loops are allowed).

Usage

IndNCStriSet(S, pt, tau, tri, M = c(1, 1, 1))

Value

I(pt is in \(\cup_{x in S} N_{CS}(x,\tau)\)), that is, returns 1 if pt is in S or inside \(N_{CS}(x,\tau)\) for at least one \(x\) in S, returns 0 otherwise where CS proximity region is constructed with respect to the triangle tri

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.

tau

A positive real number which serves as the expansion parameter in CS proximity region constructed in the triangle tri.

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

M

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

Author

Elvan Ceyhan

See Also

IndCSTeSet, IndNCStri, IndCSTe, IndNAStriSet, and IndNPEtriSet

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

set.seed(1)
dat<-runif.tri(n,Tr)$gen.points

S<-rbind(dat[1,],dat[2,])  #try also S<-c(1.5,1)

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

tau<-.5

IndNCStriSet(S,dat[3,],tau,Tr,M)
IndNCStriSet(S,dat[3,],tau=1,Tr,M)
IndNCStriSet(S,dat[3,],tau=1.5,Tr,M)

S<-rbind(dat[1,],dat[2,],dat[3,],dat[5,])
IndNCStriSet(S,dat[3,],tau,Tr,M)

IndNCStriSet(S,dat[6,],tau,Tr,M)
IndNCStriSet(S,dat[6,],tau=.25,Tr,M)

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
IndNCStriSet(S,dat[3,],tau,Tr,M)

IndNCStriSet(c(.2,.5),dat[2,],tau,Tr,M)
IndNCStriSet(dat,c(.2,.5),tau,Tr,M)
IndNCStriSet(dat,dat[2,],tau,Tr,M)
IndNCStriSet(c(.2,.5),c(.2,.5),tau,Tr,M)
IndNCStriSet(dat[5,],dat[2,],tau,Tr,M)

S<-rbind(dat[1,],dat[2,],dat[3,],dat[5,],c(.2,.5))
IndNCStriSet(S,dat[3,],tau,Tr,M)

P<-c(.4,.2)
S<-dat[c(1,3,4),]
IndNCStriSet(dat,P,tau,Tr,M)

IndNCStriSet(rbind(S,S),P,tau,Tr,M)

dat.fr<-data.frame(a=S)
IndNCStriSet(dat.fr,P,tau,Tr,M)