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 Dt 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 $M = (α, β, γ)$ 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, Dt, 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 Dt; 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.
Dt: 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

Examples

Run this code

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

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

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

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

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

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

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

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

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

IndNAStri.domset(rbind(S,S),dat,Tr,M)

dat.fr<-data.frame(a=dat)
IndNAStri.domset(S,dat.fr,Tr,M)

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