# 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 Returns $I($`S` a dominating set of PE-PCD whose vertices are the data points `Xp`$)$ for `S` in the standard equilateral triangle, that is, returns 1 if `S` is a dominating set of PE-PCD, and 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 also equivalent to the circumcenter of $T_e$). Vertices of $T_e$ are also labeled as 1, 2, and 3, respectively. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:masa-2007,ceyhan:dom-num-NPE-Spat2011,ceyhan:mcap2012;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r Idom.setPEstd.tri(S, Xp, r, M = c(1, 1, 1)) ``` ## Arguments - `S`: A set of 2D points whose PE proximity regions are considered. - `Xp`: 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 $T_e$. ## Returns $I($`S` a dominating set of PE-PCD$)$ for `S` in the standard equilateral triangle, that is, returns 1 if `S` is a dominating set of PE-PCD, and returns 0 otherwise, where PE proximity region is constructed in the standard equilateral triangle $T_e$. ## Examples ```r 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) Xp<-runif.std.tri(n)$gen.points M<-as.numeric(runif.std.tri(1)$g) #try also M<-c(.6,.2) r<-1.5 S<-rbind(Xp[1,],Xp[2,]) Idom.setPEstd.tri(S,Xp,r,M) S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,],c(.2,.5)) Idom.setPEstd.tri(S,Xp[3,],r,M) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `Idom.setPEtri` and `Idom.setCSstd.tri` ## Author(s) Elvan Ceyhan

Idom.setPEstd.tri function