# The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - one triangle case Plots the points in and outside of the triangle `tri` and also the AS proximity regions for points in data set `Xp`. AS proximity regions are defined with respect to the triangle `tri`, so AS proximity regions are defined only for points inside the triangle `tri` and vertex regions are based on the center, $M=(m_1,m_2)$ in Cartesian coordinates or $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of the triangle `tri` or based on circumcenter of `tri`; default is `M="CC"`, i.e., circumcenter of `tri`. When vertex regions are constructed with 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`. See also (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) ). ```r plotASregs.tri( Xp, tri, M = "CC", main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, vert.reg = FALSE, ... ) ``` ## Arguments - `Xp`: A set of 2D points for which AS proximity regions are constructed. - `tri`: Three 2D points, stacked row-wise, each row representing a vertex of the triangle. - `M`: The center of the triangle. `"CC"` stands for circumcenter of the triangle `tri` or a 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle $T_b$; default is `M="CC"` i.e., the circumcenter of `tri`. - `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). - `vert.reg`: A logical argument to add vertex regions to the plot, default is `vert.reg=FALSE`. - ``...``: Additional `plot` parameters. ## Returns Plot of the AS proximity regions for points inside the triangle `tri` (and only 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(1.6,1.2); plotASregs.tri(Xp0,Tr,M,main="Proximity Regions for AS-PCD", xlab="",ylab="") Xp = Xp0[1,] plotASregs.tri(Xp,Tr,M,main="Proximity Regions for AS-PCD", xlab="",ylab="") #can plot the arcs of the AS-PCD #plotASarcs.tri(Xp,Tr,M,main="Arcs of AS-PCD",xlab="",ylab="") plotASregs.tri(Xp,Tr,M,main="Proximity Regions for AS-PCD", xlab="",ylab="",vert.reg=TRUE) # or try the default center #plotASregs.tri(Xp,Tr,main="Proximity Regions for AS-PCD", xlab="",ylab="",vert.reg=TRUE); M = (arcsAStri(Xp,Tr)$param)$c #the part "M = as.numeric(arcsAStri(Xp,Tr)$param)" is optional, #for the below annotation of the plot #can add vertex labels and text to the figure (with vertex regions) #but first we need to determine whether the center used for vertex regions is CC or not #see the description for more detail. CC<-circumcenter.tri(Tr) #Arcs<-arcsAStri(Xp,Tr,M) #M = as.numeric(Arcs$parameters) if (isTRUE(all.equal(M,CC)) || identical(M,"CC")) {cent<-CC D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; Ds<-rbind(D1,D2,D3) cent.name<-"CC" } else {cent<-M cent.name<-"M" Ds<-prj.cent2edges(Tr,M) } #now we add the vertex names and annotation txt<-rbind(Tr,cent,Ds) xc<-txt[,1]+c(-.02,.03,.03,.03,.05,-0.03,-.01) yc<-txt[,2]+c(.02,.02,.02,.07,.02,.05,-.06) txt.str<-c("A","B","C",cent.name,"D1","D2","D3") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotASregs`, `plotPEregs.tri`, `plotPEregs`, `plotCSregs.tri`, and `plotCSregs` ## Author(s) Elvan Ceyhan

plotASregs.tri function