# The indices of the `M`-edge regions in a triangle that contains the points in a give data set Returns the indices of the edges whose regions contain the points in data set `Xp` in a triangle `tri`$=T(A,B,C)$ and edge 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` (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` and the corresponding edges are $1=BC$, $2=AC$, and $3=AB$. If a point in `Xp` is not inside `tri`, then the function yields `NA` as output for that entry. The corresponding edge region is the polygon with the vertex, `M`, and vertices other than the non-adjacent vertex, i.e., edge region 1 is the triangle $T(B,M,C)$, edge region 2 is $T(A,M,C)$ and edge region 3 is $T(A,B,M)$. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012,ceyhan:arc-density-CS;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r rel.edges.tri(Xp, tri, M) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points for which indices of the edge regions containing them are to be determined. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `M`: A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle `tri`. ## Returns A `list` with the elements - **re**: Indices (i.e., a `vector` of indices) of the edges whose region contains points in `Xp` in the triangle `tri` - **tri**: The vertices of the triangle, where row number corresponds to the vertex index opposite to edge whose index is given in re. - **desc**: Description of the edge labels as `"Edge labels are AB=3, BC=1, and AC=2"`. ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); M<-c(1.6,1.2) P<-c(.4,.2) rel.edges.tri(P,Tr,M) n<-20 #try also n<-40 set.seed(1) Xp<-runif.tri(n,Tr)$g M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.2) (re<-rel.edges.tri(Xp,Tr,M)) 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] if (dimension(M)==3) {M<-bary2cart(M,Tr)} #need to run this when M is given in barycentric coordinates plot(Tr,pch=".",xlab="",ylab="", main="Scatterplot of data points \n and the M-edge regions",axes=TRUE, xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) points(Xp,pch=".",col=1) L<-Tr; R<-rbind(M,M,M) segments(L[,1], L[,2], R[,1], R[,2], lty = 2) xc<-Tr[,1]+c(-.02,.03,.02) yc<-Tr[,2]+c(.02,.02,.04) txt.str<-c("A","B","C") text(xc,yc,txt.str) txt<-rbind(M,Ds) xc<-txt[,1]+c(.05,.06,-.05,-.02) yc<-txt[,2]+c(.03,.03,.05,-.08) txt.str<-c("M","re=2","re=3","re=1") text(xc,yc,txt.str) text(Xp,labels=factor(re$re)) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rel.edges.triCM`, `rel.verts.tri`, and `rel.verts.tri.nondegPE` ## Author(s) Elvan Ceyhan

rel.edges.tri function