# The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - multiple triangle case Plots the `Xp` points in and outside of the convex hull of `Yp` points and also plots the AS proximity regions for `Xp` points and Delaunay triangles based on `Yp` points. AS proximity regions are constructed with respect to the Delaunay triangles based on `Yp` points (these triangles partition the convex hull of `Yp` points), i.e., AS proximity regions are only defined for `Xp` points inside the convex hull of `Yp` points. 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. 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 plotASregs( Xp, Yp, M = "CC", main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, ... ) ``` ## Arguments - `Xp`: A set of 2D points for which AS proximity regions are constructed. - `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. - `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` and also the AS proximity regions for `Xp` points inside the convex hull of `Yp` points ## Examples ```r nx<-10 ; ny<-5 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) #or M="CC" plotASregs(Xp,Yp,M,xlab="",ylab="") plotASregs(Xp,Yp[1:3,],M,xlab="",ylab="") Xp<-c(.5,.5) plotASregs(Xp,Yp,M,xlab="",ylab="") ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotASregs.tri`, `plotPEregs.tri`, `plotPEregs`, `plotCSregs.tri`, and `plotCSregs` ## Author(s) Elvan Ceyhan

plotASregs function