# The indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) Returns $I($`p2` is in $N_{CS}(p1,t))$ for points `p1` and `p2`, that is, returns 1 if `p2` is in $NCS(p1,t)$, returns 0 otherwise, where $N_{CS}(x,t)$ is the CS proximity region for point $x$ with the expansion parameter $t>0$. CS proximity region is constructed with respect to the triangle `tri` 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 `tri` or based on the circumcenter of `tri`. `re` is the index of the edge region `p` resides, with default=`NULL` If `p1` and `p2` are distinct and either of them are outside `tri`, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r IarcCStri(p1, p2, tri, t, M, re = NULL) ``` ## Arguments - `p1`: A 2D point whose CS proximity region is constructed. - `p2`: A 2D point. The function determines whether `p2` is inside the CS proximity region of `p1` or not. - `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. - `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`. - `re`: Index of the `M`-edge region containing the point `p`, either `1,2,3` or `NULL` (default is `NULL`). ## Returns I(`p2` is in $NCS(p1,t)$) for `p1`, that is, returns 1 if `p2` is in $NCS(p1,t)$, returns 0 otherwise ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); tau<-1.5 M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.2) n<-10 set.seed(1) Xp<-runif.tri(n,Tr)$g IarcCStri(Xp[1,],Xp[2,],Tr,tau,M) P1<-as.numeric(runif.tri(1,Tr)$g) P2<-as.numeric(runif.tri(1,Tr)$g) IarcCStri(P1,P2,Tr,tau,M) #or try re<-rel.edges.tri(P1,Tr,M)$re IarcCStri(P1,P2,Tr,tau,M,re) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `IarcAStri`, `IarcPEtri`, `IarcCStri`, and `IarcCSstd.tri` ## Author(s) Elvan Ceyhan

IarcCStri function