# The alternative function for the indices of the M-vertex regions in a triangle that contains the points in a give data set An alternative function to the function `rel.verts.tri` when the center M is not the circumcenter falling outside the triangle. This function only works for a center $M$ in the interior of the triangle, with the projections of $M$ to the edges along the lines joining $M$ to the vertices. ```r rel.verts.triM(Xp, tri, M) ``` ## 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. - `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 two elements - **rv**: Indices of the vertices whose regions contains points in `Xp`. - **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); M<-c(1.6,1.0) P<-c(.4,.2) rel.verts.triM(P,Tr,M) n<-20 #try also n<-40 set.seed(1) Xp<-runif.tri(n,Tr)$g M<-c(1.6,1.0) #try also M<-c(1.3,1.3) (rv<-rel.verts.tri(Xp,Tr,M)) rel.verts.triM(rbind(Xp,c(2,2)),Tr,M) Ds<-prj.cent2edges(Tr,M) Xlim<-range(Tr[,1]) Ylim<-range(Tr[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Tr,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) points(Xp,pch=".",col=1) L<-rbind(M,M,M); R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty = 2) xc<-Tr[,1]+c(-.03,.05,.05) yc<-Tr[,2]+c(-.06,.02,.05) txt.str<-c("rv=1","rv=2","rv=3") text(xc,yc,txt.str) txt<-rbind(M,Ds) xc<-txt[,1]+c(.02,.04,-.03,0) yc<-txt[,2]+c(.07,.03,.05,-.07) txt.str<-c("M","D1","D2","D3") text(xc,yc,txt.str) text(Xp,labels=factor(rv$rv)) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rel.verts.tri` ## Author(s) Elvan Ceyhan

rel.verts.triM function