# Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case Returns the incidence matrix for the PE-PCD whose vertices are the given 3D numerical data set, `Xp`, in the tetrahedron $th=T(v=1,v=2,v=3,v=4)$. PE proximity regions are constructed with respect to tetrahedron `th` with expansion parameter $r \ge 1$ and vertex regions are based on the center `M` which is circumcenter (`"CC"`) or center of mass (`"CM"`) of `th` with default=`"CM"`. 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;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r inci.matPEtetra(Xp, th, r, M = "CM") ``` ## Arguments - `Xp`: A set of 3D points which constitute the vertices of PE-PCD. - `th`: A $4 \times 3$ matrix with each row representing a vertex of the tetrahedron. - `r`: A positive real number which serves as the expansion parameter in PE proximity region; must be $\ge 1$. - `M`: The center to be used in the construction of the vertex regions in the tetrahedron, `th`. Currently it only takes `"CC"` for circumcenter and `"CM"` for center of mass; default=`"CM"`. ## Returns Incidence matrix for the PE-PCD with vertices being 3D data set, `Xp`, in the tetrahedron `th` with vertex regions based on circumcenter or center of mass ## Examples ```r A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0); D<-c(1/2,sqrt(3)/6,sqrt(6)/3) tetra<-rbind(A,B,C,D) n<-5 Xp<-runif.tetra(n,tetra)$g #try also Xp<-c(.5,.5,.5) M<-"CM" #try also M<-"CC" r<-1.5 IM<-inci.matPEtetra(Xp,tetra,r=1.25) #uses the default M="CM" IM<-inci.matPEtetra(Xp,tetra,r=1.25,M) IM dom.num.greedy(IM) Idom.num.up.bnd(IM,3) #try also dom.num.exact(IM) #this might take a long time for large n ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `inci.matPEtri`, `inci.matPE1D`, and `inci.matPE` ## Author(s) Elvan Ceyhan

inci.matPEtetra function