pcds (version 0.1.6)

IndNAStri.domset: The indicator for the set of points S being a dominating set or not for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Description

Returns \(I(\)S a dominating set of AS-PCD\()\), that is, returns 1 if S is a dominating set of AS-PCD, returns 0 otherwise.

AS-PCD has vertex set Xp and AS proximity region is constructed with vertex regions based on the center M="CC" for circumcenter of tri; or \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of the triangle tri; default is M="CC" i.e., circumcenter of tri whose vertices are also labeled as edges 1, 2, and 3, respectively.

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).

Usage

IndNAStri.domset(S, Xp, tri, M = "CC")

Value

\(I(\)S a dominating set of AS-PCD\()\), that is, returns 1 if S is a dominating set of AS-PCD whose vertices are the data points in Xp; returns 0 otherwise, where AS proximity region is constructed in the triangle tri.

Arguments

S

A set of 2D points which is to be tested for being a dominating set for the AS-PCDs.

Xp

A set of 2D points which constitute the vertices of the AS-PCD.

tri

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

M

The center of the triangle. "CC" stands for circumcenter of the triangle tri or a 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of tri; default is M="CC" i.e., the circumcenter of tri.

Author

Elvan Ceyhan

References

See Also

IndNAStriSet, IndNPEtri.domset and IndNCStri.domset

Examples

if (FALSE) {
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);

Tr<-rbind(A,B,C);
n<-10

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

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.2)

S<-rbind(Xp[1,],Xp[2,])
IndNAStri.domset(S,Xp,Tr,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,])
IndNAStri.domset(S,Xp,Tr,M)

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
IndNAStri.domset(S,Xp,Tr,M)

IndNAStri.domset(c(.2,.5),Xp,Tr,M)
IndNAStri.domset(c(.2,.5),c(.2,.5),Tr,M)
IndNAStri.domset(Xp[5,],Xp[2,],Tr,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,],c(.2,.5))
IndNAStri.domset(S,Xp[3,],Tr,M)

IndNAStri.domset(Xp,Xp,Tr,M)

P<-c(.4,.2)
S<-Xp[c(1,3,4),]
IndNAStri.domset(Xp,P,Tr,M)
IndNAStri.domset(S,P,Tr,M)
IndNAStri.domset(S,Xp,Tr,M)

IndNAStri.domset(rbind(S,S),Xp,Tr,M)
}