# The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - multiple triangle case Plots the points in and outside of the Delaunay triangles based on `Yp` points which partition the convex hull of `Yp` points and also plots the PE proximity regions for `Xp` points and the Delaunay triangles based on `Yp` points. PE proximity regions are constructed with respect to the Delaunay triangles with the expansion parameter $r \ge 1$. Vertex regions in each triangle is based on the center $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of each Delaunay triangle or based on circumcenter of each Delaunay triangle (default for $M=(1,1,1)$ which is the center of mass of the triangle). See (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) ) for more on the PE proximity regions. Also, see (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="okabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textual",package="pcds",cached_env=.Rdpack.currefs) ) for more on Delaunay triangulation and the corresponding algorithm. ```r plotPEregs( Xp, Yp, r, M = c(1, 1, 1), asp = NA, main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, ... ) ``` ## Arguments - `Xp`: A set of 2D points for which PE proximity regions are constructed. - `Yp`: A set of 2D points which constitute the vertices of the Delaunay triangles. - `r`: A positive real number which serves as the expansion parameter in PE proximity region; must be $\ge 1$. - `M`: A 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle or circumcenter of each Delaunay triangle (for this, argument should be set as `M="CC"`), default for $M=(1,1,1)$ which is the center of mass of each triangle. - `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). - ``...``: Additional `plot` parameters. ## Returns Plot of the `Xp` points, Delaunay triangles based on `Yp` points and also the PE proximity regions for `Xp` points inside the convex hull of `Yp` points ## Examples ```r #nx is number of X points (target) and ny is number of Y points (nontarget) nx<-20; ny<-5; #try also nx<-40; ny<-10 or nx<-1000; ny<-10; set.seed(1) Xp<-cbind(runif(nx,0,1),runif(nx,0,1)) Yp<-cbind(runif(ny,0,.25), runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1)) #try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1)) M<-c(1,1,1) #try also M<-c(1,2,3) r<-1.5 #try also r<-2 plotPEregs(Xp,Yp,r,M,xlab="",ylab="") ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotPEregs.tri`, `plotASregs`, and `plotCSregs` ## Author(s) Elvan Ceyhan

plotPEregs function