# The furthest points in a data set from vertices in each $CC$-vertex region in a triangle An object of class `"Extrema"`. Returns the furthest data points among the data set, `Xp`, in each $CC$-vertex region from the vertex in the triangle, `tri`$=T(A,B,C)$. Vertex region labels/numbers correspond to the row number of the vertex in `tri`. `ch.all.intri` is for checking whether all data points are inside `tri` (default is `FALSE`). If some of the data points are not inside `tri` and `ch.all.intri=TRUE`, then the function yields an error message. If some of the data points are not inside `tri` and `ch.all.intri=FALSE`, then the function yields the closest points to edges among the data points inside `tri` (yields `NA` if there are no data points inside `tri`). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:mcap2012;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r fr2vertsCCvert.reg(Xp, tri, ch.all.intri = FALSE) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `ch.all.intri`: A logical argument (default=`FALSE`) to check whether all data points are inside the triangle `tri`. So, if it is `TRUE`, the function checks if all data points are inside the closure of the triangle (i.e., interior and boundary combined) else it does not. ## Returns A `list` with the elements - **txt1**: Vertex labels are $A=1$, $B=2$, and $C=3$ (correspond to row number in Extremum Points). - **txt2**: A short description of the distances as `"Distances from furthest points to ..."`. - **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 vertices in each $CC$-vertex region in the triangle `tri`. - **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 the triangle `tri` for this function. - **cent**: The center point used for construction of edge regions. - **ncent**: Name of the center, `cent`, it is circumcenter `"CC"` for this function - **regions**: CC-Vertex regions inside the triangle, `tri`, provided as a `list` - **region.names**: Names of the vertex regions as `"vr=1"`, `"vr=2"`, and `"vr=3"` - **region.centers**: Centers of mass of the vertex regions inside `tri` - **dist2ref**: Distances from furthest points in each vertex region to the corresponding vertex ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); n<-10 #try also n<-20 set.seed(1) Xp<-runif.tri(n,Tr)$g Ext<-fr2vertsCCvert.reg(Xp,Tr) Ext summary(Ext) plot(Ext) f2v<-Ext CC<-circumcenter.tri(Tr) #the circumcenter D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; Ds<-rbind(D1,D2,D3) Xlim<-range(Tr[,1],Xp[,1]) Ylim<-range(Tr[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Tr,xlab="",asp=1,ylab="",pch=".", main="Furthest Points in CC-Vertex Regions \n from the Vertices", axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty=2) points(Xp) points(rbind(f2v$ext),pch=4,col=2) txt<-rbind(Tr,CC,Ds) xc<-txt[,1]+c(-.06,.08,.05,.12,-.1,-.1,-.09) yc<-txt[,2]+c(.02,-.02,.05,.0,.02,.06,-.04) txt.str<-c("A","B","C","CC","D1","D2","D3") text(xc,yc,txt.str) Xp2<-rbind(Xp,c(.2,.4)) fr2vertsCCvert.reg(Xp2,Tr,ch.all.intri = FALSE) #gives an error message if ch.all.intri = TRUE #since not all points in the data set are in the triangle ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `fr2vertsCCvert.reg.basic.tri`, `fr2edgesCMedge.reg.std.tri`, `kfr2vertsCCvert.reg.basic.tri` and `kfr2vertsCCvert.reg` ## Author(s) Elvan Ceyhan

fr2vertsCCvert.reg function