# The index of the $CM$-edge region in a triangle that contains the point Returns the index of the edge whose region contains point, `p`, in the triangle `tri`$=T(A,B,C)$ with edge regions based on center of mass $CM=(A+B+C)/3$. Edges are labeled as 3 for edge $AB$, 1 for edge $BC$, and 2 for edge $AC$. If the point, `p`, is not inside `tri`, then the function yields `NA` as output. Edge region 1 is the triangle $T(B,C,CM)$, edge region 2 is $T(A,C,CM)$, and edge region 3 is $T(A,B,CM)$. 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.edge.triCM(p, tri) ``` ## Arguments - `p`: A 2D point for which $CM$-edge region it resides in is to be determined in the triangle `tri`. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. ## Returns A `list` with three elements - **re**: Index of the $CM$-edge region that contains point, `p` in the triangle `tri`. - **tri**: The vertices of the triangle, where row labels are $A$, $B$, and $C$ with edges are labeled as 3 for edge $AB$, 1 for edge $BC$, and 2 for edge $AC$. - **desc**: Description of the edge labels ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); P<-c(1.4,1.2) rel.edge.triCM(P,Tr) P<-c(1.5,1.61) rel.edge.triCM(P,Tr) CM<-(A+B+C)/3 n<-20 #try also n<-40 Xp<-runif.tri(n,Tr)$g re<-vector() for (i in 1:n) re<-c(re,rel.edge.triCM(Xp[i,],Tr)$re) re 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="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) points(Xp,pch=".") polygon(Tr) L<-Tr; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE) segments(L[,1], L[,2], R[,1], R[,2], lty = 2) text(Xp,labels=factor(re)) txt<-rbind(Tr,CM) xc<-txt[,1] yc<-txt[,2] txt.str<-c("A","B","C","CM") text(xc,yc,txt.str) p1<-(A+B+CM)/3 p2<-(B+C+CM)/3 p3<-(A+C+CM)/3 plot(Tr,xlab="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) L<-Tr; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE) segments(L[,1], L[,2], R[,1], R[,2], lty = 2) txt<-rbind(Tr,CM,p1,p2,p3) xc<-txt[,1]+c(-.02,.02,.02,.02,.02,.02,.02) yc<-txt[,2]+c(.02,.02,.04,.05,.02,.02,.02) txt.str<-c("A","B","C","CM","re=3","re=1","re=2") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rel.edge.tri`, `rel.edge.basic.triCM`, `rel.edge.basic.tri`, `rel.edge.std.triCM`, and `edge.reg.triCM` ## Author(s) Elvan Ceyhan

rel.edge.triCM function