# The index of the edge region in the standard equilateral triangle that contains a point Returns the index of the edge whose region contains point, `p`, in the standard equilateral triangle $T_e=T(A=(0,0),B=(1,0),C=(1/2,\sqrt{3}/2))$ 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 $T(B,C,M)$, edge region 2 is $T(A,C,M)$, 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.edge.std.triCM(p) ``` ## Arguments - `p`: A 2D point for which $CM$-edge region it resides in is to be determined in the the standard equilateral triangle $T_e$. ## Returns A `list` with three elements - **re**: Index of the $CM$-edge region that contains point, `p` in the standard equilateral triangle $T_e$ - **tri**: The vertices of the standard equilateral triangle $T_e$, 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 P<-c(.4,.2) rel.edge.std.triCM(P) A<-c(0,0); B<-c(1,0); C<-c(0.5,sqrt(3)/2); Te<-rbind(A,B,C) D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; CM<-(A+B+C)/3 n<-20 #try also n<-40 Xp<-runif.std.tri(n)$gen.points re<-vector() for (i in 1:n) re<-c(re,rel.edge.std.triCM(Xp[i,])$re) re Xlim<-range(Te[,1],Xp[,1]) Ylim<-range(Te[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Te,asp=1,xlab="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01)) points(Xp,pch=".") polygon(Te) L<-Te; 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(Te,CM) xc<-txt[,1]+c(-.03,.03,.03,-.06) yc<-txt[,2]+c(.02,.02,.02,.03) 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(Te,xlab="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01)) polygon(Te) L<-Te; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE) segments(L[,1], L[,2], R[,1], R[,2], lty = 2) txt<-rbind(Te,CM,p1,p2,p3) xc<-txt[,1]+c(-.03,.03,.03,-.06,0,0,0) yc<-txt[,2]+c(.02,.02,.02,.03,0,0,0) 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.triCM`, `rel.edge.tri`, `rel.edge.basic.triCM`, `rel.edge.basic.tri`, and `edge.reg.triCM` ## Author(s) Elvan Ceyhan

rel.edge.std.triCM function