1d:T7d2,# Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case Returns the incidence matrix of the AS-PCD whose vertices are the given 2D numerical data set, `Xp`, in the triangle `tri`$=T(v=1,v=2,v=3)$. AS proximity regions are defined with respect to the triangle `tri`$=T(v=1,v=2,v=3)$ 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 the triangle `tri` or based on circumcenter of `tri`; default is `M="CC"`, i.e., circumcenter of `tri`. Loops are allowed, so the diagonal entries are all equal to 1. 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 inci.matAStri(Xp, tri, M = "CC") ``` ## Arguments - `Xp`: A set of 2D points which constitute the vertices of 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 Incidence matrix for the AS-PCD whose vertices are the 2D data set, `Xp`, and AS proximity regions are defined with respect to the triangle `tri` and vertex regions based on the center `M`. ## 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)$g M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.2) IM<-inci.matAStri(Xp,Tr,M) IM dom.num.greedy(IM) dom.num.exact(IM) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `inci.matAS`, `inci.matPEtri`, and `inci.matCStri` ## Author(s) Elvan Ceyhan

inci.matAStri function