# 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 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 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` or based on circumcenter of `tri`; default is `M="CC"`, i.e., circumcenter of `tri` whose vertices are also labeled as edges 1, 2, and 3, respectively. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r Idom.setAStri(S, Xp, tri, M = "CC") ``` ## 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`. ## Returns $I($`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`. ## Examples ```r 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,]) Idom.setAStri(S,Xp,Tr,M) S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,]) Idom.setAStri(S,Xp,Tr,M) S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3)) Idom.setAStri(S,Xp,Tr,M) Idom.setAStri(c(.2,.5),Xp,Tr,M) Idom.setAStri(c(.2,.5),c(.2,.5),Tr,M) Idom.setAStri(Xp[5,],Xp[2,],Tr,M) S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,],c(.2,.5)) Idom.setAStri(S,Xp[3,],Tr,M) Idom.setAStri(Xp,Xp,Tr,M) P<-c(.4,.2) S<-Xp[c(1,3,4),] Idom.setAStri(Xp,P,Tr,M) Idom.setAStri(S,P,Tr,M) Idom.setAStri(S,Xp,Tr,M) Idom.setAStri(rbind(S,S),Xp,Tr,M) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `IarcASset2pnt.tri`, `Idom.setPEtri` and `Idom.setCStri` ## Author(s) Elvan Ceyhan

Idom.setAStri function