pcds (version 0.1.4)

IndNPETe.domset: The indicator for the set of points S being a dominating set or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

Description

Returns \(I(\)S a dominating set of PE-PCD whose vertices are the data points Dt\()\), that is, returns 1 if S is a dominating set of PE-PCD, 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 expansion parameter \(r \ge 1\) and vertex 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 \(T_e\); default is \(M=(1,1,1)\) i.e., the center of mass of \(T_e\) (which is equivalent to the circumcenter of \(T_e\)). Vertices of \(T_e\) are also labeled as 1, 2, and 3, respectively.

See also (ceyhan:Phd-thesis,ceyhan:masa-2007,ceyhan:dom-num-NPE-Spat2011,ceyhan:mcap2012;textualpcds).

Usage

IndNPETe.domset(S, Dt, r, M = c(1, 1, 1))

Value

\(I(\)S a dominating set of PE-PCD\()\), that is, returns 1 if S is a dominating set of PE-PCD, returns 0 otherwise, where PE proximity region is constructed in the standard equilateral triangle \(T_e\)

Arguments

S

A set of 2D points whose PE proximity regions are considered.

Dt

A set of 2D points which constitutes the vertices of the PE-PCD.

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 \(T_e\).

Author

Elvan Ceyhan

References

See Also

IndNPEtri.domset and IndCSTe.domset

Examples

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,])
IndNPETe.domset(S,dat,r,M)

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

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
IndNPETe.domset(S,dat,r,M)

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

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

IndNPETe.domset(dat,dat,r,M)

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

IndNPETe.domset(rbind(S,S),dat,r,M)

dat.fr<-data.frame(a=dat)
IndNPETe.domset(S,dat.fr,r,M)