# The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - one triangle case Plots the points in and outside of the triangle `tri` and also the PE proximity regions for points in data set `Xp`. PE proximity regions are defined with respect to the triangle `tri` with expansion parameter $r \ge 1$, so PE proximity regions are defined only for points inside the triangle `tri`. Vertex regions are 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`. When the center is the circumcenter, `CC`, the vertex regions are constructed based on the orthogonal projections to the edges, while with any interior center `M`, the vertex regions are constructed using the extensions of the lines combining vertices with `M`. `M`-vertex regions are recommended spatial inference, due to geometry invariance property of the arc density and domination number the PE-PCDs based on uniform data. 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 plotPEregs.tri( Xp, tri, r, M = c(1, 1, 1), asp = NA, main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, vert.reg = FALSE, ... ) ``` ## Arguments - `Xp`: A set of 2D points for which PE proximity regions are constructed. - `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`. - `asp`: A `numeric` value, giving the aspect ratio $y/x$ (default is `NA`), see the official help page for `asp` by typing "`? asp`". - `main`: An overall title for the plot (default=`NULL`). - `xlab, ylab`: Titles for the $x$ and $y$ axes, respectively (default=`NULL` for both). - `xlim, ylim`: Two `numeric` vectors of length 2, giving the $x$- and $y$-coordinate ranges (default=`NULL` for both). - `vert.reg`: A logical argument to add vertex regions to the plot, default is `vert.reg=FALSE`. - ``...``: Additional `plot` parameters. ## Returns Plot of the PE proximity regions for points inside the triangle `tri` (and just the points outside `tri`) ## 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) Xp0<-runif.tri(n,Tr)$g M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.0) or M = circumcenter.tri(Tr) r<-1.5 #try also r<-2 plotPEregs.tri(Xp0,Tr,r,M) Xp = Xp0[1,] plotPEregs.tri(Xp,Tr,r,M) plotPEregs.tri(Xp,Tr,r,M, main="PE Proximity Regions with r = 1.5", xlab="",ylab="",vert.reg = TRUE) # or try the default center #plotPEregs.tri(Xp,Tr,r,main="PE Proximity Regions with r = 1.5",xlab="",ylab="",vert.reg = TRUE); #M=(arcsPEtri(Xp,Tr,r)$param)$c #the part "M=(arcsPEtri(Xp,Tr,r)$param)$cent" is optional, #for the below annotation of the plot #can add vertex labels and text to the figure (with vertex regions) ifelse(isTRUE(all.equal(M,circumcenter.tri(Tr))), {Ds<-rbind((B+C)/2,(A+C)/2,(A+B)/2); cent.name="CC"}, {Ds<-prj.cent2edges(Tr,M); cent.name<-"M"}) txt<-rbind(Tr,M,Ds) xc<-txt[,1]+c(-.02,.02,.02,.02,.03,-0.03,-.01) yc<-txt[,2]+c(.02,.02,.02,.07,.02,.05,-.06) txt.str<-c("A","B","C",cent.name,"D1","D2","D3") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotPEregs`, `plotASregs.tri`, and `plotCSregs.tri` ## Author(s) Elvan Ceyhan

plotPEregs.tri function