# The vertices of the $CM$-edge region in a triangle that contains the point Returns the edge whose region contains point, `p`, in the triangle `tri`$=T(A,B,C)$ with edge regions based on center of mass $CM=(A+B+C)/3$. This function is related to `rel.edge.triCM`, but unlike `rel.edge.triCM` the related edges are given as vertices `ABC` for $re=3$, as `BCA` for $re=1$ and as `CAB` for $re=2$ where edges are labeled as 3 for edge $AB$, 1 for edge $BC$, and 2 for edge $AC$. The vertices are given one vertex in each row in the output, e.g., $ABC$ is printed as `rbind(A,B,C)`, where row 1 has the entries of vertex A, row 2 has the entries of vertex B, and row 3 has the entries of vertex C. If the point, `p`, is not inside `tri`, then the function yields `NA` as output. Edge region for BCA is the triangle $T(B,C,CM)$, edge region CAB is $T(A,C,CM)$, and edge region ABC 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;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r edge.reg.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 The $CM$-edge region that contains point, `p` in the triangle `tri`. The related edges are given as vertices `ABC` for $re=3$, as `BCA` for $re=1$ and as `CAB` for $re=2$ where edges are labeled as 3 for edge $AB$, 1 for edge $BC$, and 2 for edge $AC$. ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); P<-c(.4,.2) #try also P<-as.numeric(runif.tri(1,Tr)$g) edge.reg.triCM(P,Tr) P<-c(1.8,.5) edge.reg.triCM(P,Tr) CM<-(A+B+C)/3 p1<-(A+B+CM)/3 p2<-(B+C+CM)/3 p3<-(A+C+CM)/3 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) 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,-.05,0,0,0) yc<-txt[,2]+c(.02,.02,.02,.02,0,0,0) txt.str<-c("A","B","C","CM","re=T(A,B,CM)","re=T(B,C,CM)","re=T(A,C,CM)") 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.triCM`, `rel.edge.basic.triCM`, `rel.edge.basic.tri`, `rel.edge.std.triCM`, and `edge.reg.triCM` ## Author(s) Elvan Ceyhan

edge.reg.triCM function