# The closest points to circumcenter in each $CC$-vertex region in a standard basic triangle An object of class `"Extrema"`. Returns the closest data points among the data set, `Xp`, to circumcenter, $CC$, in each $CC$-vertex region in the standard basic triangle $T_b = T(A=(0,0),B=(1,0),C=(c_1,c_2))=$(vertex 1,vertex 2,vertex 3). `ch.all.intri` is for checking whether all data points are inside $T_b$ (default is `FALSE`). 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 cl2CCvert.reg.basic.tri(Xp, c1, c2, ch.all.intri = FALSE) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points. - `c1, c2`: Positive real numbers which constitute the vertex of the standard basic triangle. adjacent to the shorter edges; $c_1$ must be in $[0,1/2]$, $c_2>0$ and $(1-c_1)^2+c_2^2 \le 1$ - `ch.all.intri`: A logical argument for checking whether all data points are inside $T_b$ (default is `FALSE`). ## 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 closest points to ..."`. - **type**: Type of the extrema points - **mtitle**: The `"main"` title for the plot of the extrema - **ext**: The extrema points, here, closest points to $CC$ in each vertex 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 $T_b$. - **cent**: The center point used for construction of vertex regions - **ncent**: Name of the center, `cent`, it is `"CC"` for this function. - **regions**: Vertex regions inside the triangle, $T_b$, 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 $T_b$. - **dist2ref**: Distances from closest points in each vertex region to CC. ## Examples ```r c1<-.4; c2<-.6; A<-c(0,0); B<-c(1,0); C<-c(c1,c2); Tb<-rbind(A,B,C) n<-15 set.seed(1) Xp<-runif.basic.tri(n,c1,c2)$g Ext<-cl2CCvert.reg.basic.tri(Xp,c1,c2) Ext summary(Ext) plot(Ext) c2CC<-Ext CC<-circumcenter.basic.tri(c1,c2) #the circumcenter D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; Ds<-rbind(D1,D2,D3) Xlim<-range(Tb[,1],Xp[,1]) Ylim<-range(Tb[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(A,pch=".",asp=1,xlab="",ylab="", main="Closest Points in CC-Vertex Regions \n to the Circumcenter", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tb) L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty=2) points(Xp) points(c2CC$ext,pch=4,col=2) txt<-rbind(Tb,CC,Ds) xc<-txt[,1]+c(-.03,.03,.02,.07,.06,-.05,.01) yc<-txt[,2]+c(.02,.02,.03,-.01,.03,.03,-.04) txt.str<-c("A","B","C","CC","D1","D2","D3") text(xc,yc,txt.str) Xp2<-rbind(Xp,c(.2,.4)) cl2CCvert.reg.basic.tri(Xp2,c1,c2,ch.all.intri = FALSE) #gives an error message if ch.all.intri = TRUE #since not all points are in the standard basic triangle ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `cl2CCvert.reg`, `cl2edges.vert.reg.basic.tri`, `cl2edgesMvert.reg`, `cl2edgesCMvert.reg`, and `fr2edgesCMedge.reg.std.tri` ## Author(s) Elvan Ceyhan

cl2CCvert.reg.basic.tri function