# The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case Plots the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) whose vertices are the data points in `Xp` in the multiple triangle case and the Delaunay triangles based on `Yp` points. If there are duplicates of `Xp` points, only one point is retained for each duplicate value, and a warning message is printed. PE proximity regions are defined with respect to the Delaunay triangles based on `Yp` points with expansion parameter $r \ge 1$ and vertex regions in each triangle are 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). Convex hull of `Yp` is partitioned by the Delaunay triangles based on `Yp` points (i.e., multiple triangles are the set of these Delaunay triangles whose union constitutes the convex hull of `Yp` points). Loops are not allowed so arcs are only possible for points inside the convex hull of `Yp` points. 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-PCDs. 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 plotPEarcs( 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 which constitute the vertices of the PE-PCD. - `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 A plot of the arcs of the PE-PCD whose vertices are the points in data set `Xp` and the Delaunay triangles based on `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 plotPEarcs(Xp,Yp,r,M,xlab="",ylab="") ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotPEarcs.tri`, `plotASarcs`, and `plotCSarcs` ## Author(s) Elvan Ceyhan

plotPEarcs function