# The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - one triangle case Plots the arcs of AS-PCD whose vertices are the data points, `Xp` and also the triangle `tri`. AS proximity regions are constructed with respect to the triangle `tri`, i.e., only for `Xp` points inside the triangle `tri`. 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, $M=(m_1,m_2)$ 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 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`. 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 plotASarcs.tri( Xp, tri, M = "CC", asp = NA, main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, vert.reg = FALSE, ... ) ``` ## Arguments - `Xp`: A set of 2D points which constitute the vertices of the AS-PCD. - `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`. - `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). - `vert.reg`: A logical argument to add vertex regions to the plot, default is `vert.reg=FALSE`. - ``...``: 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 triangle `tri`; also plots the triangle `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) Xp<-runif.tri(n,Tr)$g #try also Xp<-cbind(runif(n,1,2),runif(n,0,2)) M<-as.numeric(runif.tri(1,Tr)$g) #try also #M<-c(1.6,1.2) plotASarcs.tri(Xp,Tr,M,main="Arcs of AS-PCD",xlab="",ylab="") plotASarcs.tri(Xp,Tr,M,main="Arcs of AS-PCD",xlab="",ylab="",vert.reg = TRUE) # or try the default center #plotASarcs.tri(Xp,Tr,asp=1,main="arcs of 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) 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,.02,.02,.01,.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 `plotASarcs`, `plotPEarcs.tri`, `plotPEarcs`, `plotCSarcs.tri`, and `plotCSarcs` ## Author(s) Elvan Ceyhan

plotASarcs.tri function