# The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - one triangle case Plots the points in and outside of the triangle `tri` and also the CS proximity regions which are also triangular for points inside the triangle `tri` with edge regions are based on the center of mass CM. CS proximity regions are defined with respect to the triangle `tri` with expansion parameter $t>0$, so CS proximity regions are defined only for points inside the triangle `tri`. Edge 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`; default is $M=(1,1,1)$ i.e., the center of mass of `tri`. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r plotCSregs.tri( Xp, tri, t, M = c(1, 1, 1), asp = NA, main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, edge.reg = FALSE, ... ) ``` ## Arguments - `Xp`: A set of 2D points for which CS proximity regions are constructed. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `t`: A positive real number which serves as the expansion parameter in CS proximity region. - `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`; 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). - `edge.reg`: A logical argument to add edge regions to the plot, default is `edge.reg=FALSE`. - ``...``: Additional `plot` parameters. ## Returns Plot of the CS 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) t<-.5 #try also t<-2 plotCSregs.tri(Xp0,Tr,t,M,main="Proximity Regions for CS-PCD", xlab="",ylab="") Xp = Xp0[1,] plotCSregs.tri(Xp,Tr,t,M,main="CS Proximity Regions with t=.5", xlab="",ylab="",edge.reg=TRUE) # or try the default center plotCSregs.tri(Xp,Tr,t,main="CS Proximity Regions with t=.5", xlab="",ylab="",edge.reg=TRUE); #M=(arcsCStri(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 edge regions) txt<-rbind(Tr,M) xc<-txt[,1]+c(-.02,.02,.02,.02) yc<-txt[,2]+c(.02,.02,.02,.03) txt.str<-c("A","B","C","M") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotCSregs`, `plotASregs.tri` and `plotPEregs.tri`, ## Author(s) Elvan Ceyhan

plotCSregs.tri function