# The indicator for the set of points `S` being a dominating set or not for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case Returns $I($`S` a dominating set of CS-PCD whose vertices are the data set `Xp`$)$, that is, returns 1 if `S` is a dominating set of CS-PCD, 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`. The triangle `tri`$=T(A,B,C)$ has edges $AB$, $BC$, $AC$ which are also labeled as edges 3, 1, and 2, respectively. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:mcap2012;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r Idom.setCStri(S, Xp, tri, t, M = c(1, 1, 1)) ``` ## Arguments - `S`: A set of 2D points which is to be tested for being a dominating set for the CS-PCDs. - `Xp`: A set of 2D points which constitute the vertices of the CS-PCD. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `t`: A positive real number which serves as the expansion parameter in CS proximity region constructed in the triangle `tri`. - `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`. ## Returns $I($`S` a dominating set of the CS-PCD$)$, that is, returns 1 if `S` is a dominating set of CS-PCD whose vertices are the data points in `Xp`; returns 0 otherwise, where CS 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(1.6,1.0) tau<-.5 S<-rbind(Xp[1,],Xp[2,]) Idom.setCStri(S,Xp,Tr,tau,M) S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,]) Idom.setCStri(S,Xp,Tr,tau,M) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `Idom.setCSstd.tri`, `Idom.setPEtri` and `Idom.setAStri` ## Author(s) Elvan Ceyhan

Idom.setCStri function