# The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case Plots the arcs of AS-PCD whose vertices are the data points in `Xp` and Delaunay triangles based on `Yp` points. AS proximity regions are constructed with respect to the Delaunay triangles based on `Yp` points, i.e., AS proximity regions are defined only for `Xp` points inside the convex hull of `Yp` points. That is, arcs may exist for `Xp` points only inside the convex hull of `Yp` points. If there are duplicates of `Xp` points, only one point is retained for each duplicate value, and a warning message is printed. Vertex regions are based on the center `M="CC"` for circumcenter of each Delaunay triangle or $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of each Delaunay triangle; default is `M="CC"` i.e., circumcenter of each triangle. 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`. 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:comp-geo-2010,ceyhan:mcap2012;textual",package="pcds",cached_env=.Rdpack.currefs) ) for more on AS-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 plotASarcs( Xp, Yp, M = "CC", 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 AS-PCD. - `Yp`: A set of 2D points which constitute the vertices of the Delaunay triangulation. The Delaunay triangles partition the convex hull of `Yp` points. - `M`: The center of the triangle. `"CC"` stands for circumcenter of each Delaunay triangle or 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle; default is `M="CC"` i.e., the circumcenter of each triangle. - `asp`: A `numeric` value, giving the aspect ratio for $y$ axis to $x$-axis $y/x$ (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 AS-PCD for a 2D data set `Xp` where AS proximity regions are defined with respect to the Delaunay triangles based on `Yp` points; also plots 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<-15; 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) plotASarcs(Xp,Yp,M,asp=1,xlab="",ylab="") plotASarcs(Xp,Yp[1:3,],M,asp=1,xlab="",ylab="") ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotASarcs.tri`, `plotPEarcs.tri`, `plotPEarcs`, `plotCSarcs.tri`, and `plotCSarcs` ## Author(s) Elvan Ceyhan

plotASarcs function