# The furthest points in a data set from edges in each $CM$-edge region in the standard equilateral triangle An object of class `"Extrema"`. Returns the furthest data points among the data set, `Xp`, in each $CM$-edge region from the edge in the standard equilateral triangle $T_e=T(A=(0,0),B=(1,0),C=(1/2,\sqrt{3}/2))$. `ch.all.intri` is for checking whether all data points are inside $T_e$ (default is `FALSE`). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r fr2edgesCMedge.reg.std.tri(Xp, ch.all.intri = FALSE) ``` ## Arguments - `Xp`: A set of 2D points, some could be inside and some could be outside standard equilateral triangle $T_e$. - `ch.all.intri`: A logical argument used for checking whether all data points are inside $T_e$ (default is `FALSE`). ## Returns A `list` with the elements - **txt1**: Edge labels as $AB=3$, $BC=1$, and $AC=2$ for $T_e$ (correspond to row number in Extremum Points). - **txt2**: A short description of the distances as `"Distances to Edges"`. - **type**: Type of the extrema points - **desc**: A short description of the extrema points - **mtitle**: The `"main"` title for the plot of the extrema - **ext**: The extrema points, here, furthest points from edges in each edge region. - **X**: The input data, `Xp`, can be a `matrix` or `data frame` - **num.points**: The number of data points, i.e., size of `Xp` - **supp**: Support of the data points, here, it is $T_e$. - **cent**: The center point used for construction of edge regions. - **ncent**: Name of the center, `cent`, it is center of mass `"CM"` for this function. - **regions**: Edge regions inside the triangle, $T_e$, provided as a list. - **region.names**: Names of the edge regions as `"er=1"`, `"er=2"`, and `"er=3"`. - **region.centers**: Centers of mass of the edge regions inside $T_e$. - **dist2ref**: Distances from furthest points in each edge region to the corresponding edge. ## Examples ```r n<-20 Xp<-runif.std.tri(n)$gen.points Ext<-fr2edgesCMedge.reg.std.tri(Xp) Ext summary(Ext) plot(Ext,asp=1) ed.far<-Ext Xp2<-rbind(Xp,c(.8,.8)) fr2edgesCMedge.reg.std.tri(Xp2) fr2edgesCMedge.reg.std.tri(Xp2,ch.all.intri = FALSE) #gives error if ch.all.intri = TRUE A<-c(0,0); B<-c(1,0); C<-c(0.5,sqrt(3)/2); Te<-rbind(A,B,C) CM<-(A+B+C)/3 p1<-(A+B)/2 p2<-(B+C)/2 p3<-(A+C)/2 Xlim<-range(Te[,1],Xp[,1]) Ylim<-range(Te[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(A,pch=".",xlab="",ylab="", main="Furthest Points in CM-Edge Regions \n of Std Equilateral Triangle from its Edges", axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Te) L<-Te; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE) segments(L[,1], L[,2], R[,1], R[,2], lty=2) points(Xp,xlab="",ylab="") points(ed.far$ext,pty=2,pch=4,col="red") txt<-rbind(Te,CM,p1,p2,p3) xc<-txt[,1]+c(-.03,.03,.03,-.06,0,0,0) yc<-txt[,2]+c(.02,.02,.02,.02,0,0,0) txt.str<-c("A","B","C","CM","re=2","re=3","re=1") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `fr2vertsCCvert.reg.basic.tri`, `fr2vertsCCvert.reg`, `fr2vertsCCvert.reg.basic.tri`, `kfr2vertsCCvert.reg`, and `cl2edges.std.tri` ## Author(s) Elvan Ceyhan

fr2edgesCMedge.reg.std.tri function