# The vertices of the Proportional Edge (PE) Proximity Region in a general triangle Returns the vertices of the PE proximity region (which is itself a triangle) for a point in the triangle `tri`$=T(A,B,C)=$`(rv=1,rv=2,rv=3)`. PE proximity region is defined with respect to the triangle `tri` with expansion parameter $r \ge 1$ and vertex regions based on 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 the circumcenter of `tri`; default is $M=(1,1,1)$, i.e., the center of mass of `tri`. Vertex regions are labeled as $1,2,3$ rowwise for the vertices of the triangle `tri`. `rv` is the index of the vertex region `p` resides, with default=`NULL`. If `p` is outside of `tri`, it returns `NULL` for the proximity region. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:arc-density-PE,ceyhan:dom-num-NPE-Spat2011;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r NPEtri(p, tri, r, M = c(1, 1, 1), rv = NULL) ``` ## Arguments - `p`: A 2D point whose PE proximity region is to be computed. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `r`: A positive real number which serves as the expansion parameter in PE proximity region; 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 triangle `tri` or the circumcenter of `tri` which may be entered as "CC" as well; default is $M=(1,1,1)$, i.e., the center of mass of `tri`. - `rv`: Index of the `M`-vertex region containing the point `p`, either `1,2,3` or `NULL` (default is `NULL`). ## Returns Vertices of the triangular region which constitutes the PE proximity region with expansion parameter `r` and center `M` for a point `p` ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.0) r<-1.5 n<-3 set.seed(1) Xp<-runif.tri(n,Tr)$g NPEtri(Xp[3,],Tr,r,M) P1<-as.numeric(runif.tri(1,Tr)$g) #try also P1<-c(.4,.2) NPEtri(P1,Tr,r,M) M<-c(1.3,1.3) r<-2 P1<-c(1.4,1.2) P2<-c(1.5,1.26) NPEtri(P1,Tr,r,M) NPEtri(P2,Tr,r,M) #or try Rv<-rel.vert.tri(P1,Tr,M)$rv NPEtri(P1,Tr,r,M,Rv) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `NPEbasic.tri`, `NAStri`, `NCStri`, and `IarcPEtri` ## Author(s) Elvan Ceyhan

NPEtri function