# An alternative to the function `IarcCStri` which yields 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 $N_{CS}(p1,t)$, 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 of mass, $CM$. `re` is the index of the $CM$-edge region `p` resides, with default=`NULL` but must be provided as vertices $(y_1,y_2,y_3)$ for $re=3$ as rbind(y2,y3,y1) for $re=1$ and as rbind(y1,y3,y2) for $re=2$ for triangle $T(y_1,y_2,y_3)$. 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.alt(p1, p2, tri, t, 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. - `re`: Index of the $CM$-edge region containing the point `p`, either `1,2,3` or `NULL`, default=`NULL` but must be provided (row-wise) as vertices $(y_1,y_2,y_3)$ for `re=3` as $(y_2,y_3,y_1)$ for `re=1` and as $(y_1,y_3,y_2)$ for `re=2` for triangle $T(y_1,y_2,y_3)$. ## Returns $I($`p2` is in $N_{CS}(p1,t))$ for `p1`, that is, returns 1 if `p2` is in $N_{CS}(p1,t)$, returns 0 otherwise. ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.6,2); Tr<-rbind(A,B,C); t<-1.5 P1<-c(.4,.2) P2<-c(1.8,.5) IarcCStri(P1,P2,Tr,t,M=c(1,1,1)) IarcCStri.alt(P1,P2,Tr,t) IarcCStri(P2,P1,Tr,t,M=c(1,1,1)) IarcCStri.alt(P2,P1,Tr,t) #or try re<-rel.edges.triCM(P1,Tr)$re IarcCStri(P1,P2,Tr,t,M=c(1,1,1),re) IarcCStri.alt(P1,P2,Tr,t,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.alt function