# The indices of the $CC$-vertex regions in a triangle that contains the points in a give data set. Returns the indices of the vertices whose regions contain the points in data set `Xp` in a triangle `tri`$=(A,B,C)$ and vertex regions are based on the circumcenter $CC$ of `tri`. (see the plots in the example for illustrations). The vertices of the triangle `tri` are labeled as $1=A$, $2=B$, and $3=C$ also according to the row number the vertex is recorded in `tri`. If a point in `Xp` is not inside `tri`, then the function yields `NA` as output. The corresponding vertex region is the polygon whose interior points are closest to that vertex. If `tri` is equilateral triangle, then $CC$ and $CM$ (center of mass) coincide. 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 rel.verts.triCC(Xp, tri) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points for which indices of the vertex regions containing them are to be determined. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. ## Returns A `list` with two elements - **rv**: Indices (i.e., a `vector` of indices) of the vertices whose region contains points in `Xp` in the triangle `tri` - **tri**: The vertices of the triangle, where row number corresponds to the vertex index in `rv`. ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); P<-c(.4,.2) rel.verts.triCC(P,Tr) n<-20 #try also n<-40 set.seed(1) Xp<-runif.tri(n,Tr)$g rel.verts.triCC(Xp,Tr) rel.verts.triCC(rbind(Xp,c(2,2)),Tr) (rv<-rel.verts.triCC(Xp,Tr)) CC<-circumcenter.tri(Tr) D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; Ds<-rbind(D1,D2,D3) Xlim<-range(Tr[,1],Xp[,1],CC[1]) Ylim<-range(Tr[,2],Xp[,2],CC[2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Tr,pch=".",asp=1,xlab="",ylab="", main="Scatterplot of data points \n and the CC-vertex regions", axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) points(Xp,pch=".",col=1) L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty = 2) xc<-Tr[,1] yc<-Tr[,2] txt.str<-c("rv=1","rv=2","rv=3") text(xc,yc,txt.str) txt<-rbind(CC,Ds) xc<-txt[,1]+c(.04,.04,-.03,0) yc<-txt[,2]+c(-.07,.04,.06,-.08) txt.str<-c("CC","D1","D2","D3") text(xc,yc,txt.str) text(Xp,labels=factor(rv$rv)) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rel.verts.triCM`, `rel.verts.tri`, and `rel.verts.tri.nondegPE` ## Author(s) Elvan Ceyhan

rel.verts.triCC function