# Returns the ranks and orders of points in decreasing distance to the edges of the triangle Two functions: `rank.dist2edges.std.tri` and `order.dist2edges.std.tri`. `rank.dist2edges.std.tri` finds the ranks of the distances of points in data, `Xp`, to the edges of the standard equilateral triangle $T_e=T((0,0),(1,0),(1/2,\sqrt{3}/2))$ `dec` is a logical argument, default is `TRUE`, so the ranks are for decreasing distances, if `FALSE` it will be in increasing distances. `order.dist2edges.std.tri` finds the orders of the distances of points in data, `Xp`, to the edges of $T_e$. The arguments are as in `rank.dist2edges.std.tri`. ```r rank.dist2edges.std.tri(Xp, dec = TRUE) order.dist2edges.std.tri(Xp, dec = TRUE) ``` ## Arguments - `Xp`: A set of 2D points representing the data set in which ranking in terms of the distance to the edges of $T_e$ is performed. - `dec`: A logical argument indicating the how the ranking will be performed. If `TRUE`, the ranks are for decreasing distances, and if `FALSE` they will be in increasing distances, default is `TRUE`. ## Returns A `list` with two elements - **distances**: Distances from data points to the edges of $T_e$ - **dist.rank**: The ranks of the data points in decreasing distances to the edges of $T_e$ ## Examples ```r #Examples for rank.dist2edges.std.tri n<-10 set.seed(1) Xp<-runif.std.tri(n)$gen.points dec.dist<-rank.dist2edges.std.tri(Xp) dec.dist dec.dist.rank<-dec.dist[[2]] #the rank of distances to the edges in decreasing order dec.dist.rank A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C); Xlim<-range(Te[,1]) Ylim<-range(Te[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(A,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.0,.01), ylim=Ylim+yd*c(-.01,.01)) polygon(Te) points(Xp,pch=".") text(Xp,labels = factor(dec.dist.rank) ) inc.dist<-rank.dist2edges.std.tri(Xp,dec = FALSE) inc.dist inc.dist.rank<-inc.dist[[2]] #the rank of distances to the edges in increasing order inc.dist.rank dist<-inc.dist[[1]] #distances to the edges of the std eq. triangle dist plot(A,pch=".",xlab="",ylab="",xlim=Xlim,ylim=Ylim) polygon(Te) points(Xp,pch=".",xlab="",ylab="", main="",xlim=Xlim+xd*c(-.05,.05), ylim=Ylim+yd*c(-.05,.05)) text(Xp,labels = factor(inc.dist.rank)) #Examples for order.dist2edges.std.tri n<-10 set.seed(1) Xp<-runif.std.tri(n)$gen.points #try also Xp<-cbind(runif(n),runif(n)) dec.dist<-order.dist2edges.std.tri(Xp) dec.dist dec.dist.order<-dec.dist[[2]] #the order of distances to the edges in decreasing order dec.dist.order A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C); Xlim<-range(Te[,1]) Ylim<-range(Te[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(A,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.01,.01), ylim=Ylim+yd*c(-.01,.01)) polygon(Te) points(Xp,pch=".") text(Xp[dec.dist.order,],labels = factor(1:n) ) inc.dist<-order.dist2edges.std.tri(Xp,dec = FALSE) inc.dist inc.dist.order<-inc.dist[[2]] #the order of distances to the edges in increasing order inc.dist.order dist<-inc.dist[[1]] #distances to the edges of the std eq. triangle dist dist[inc.dist.order] #distances in increasing order plot(A,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05), ylim=Ylim+yd*c(-.05,.05)) polygon(Te) points(Xp,pch=".") text(Xp[inc.dist.order,],labels = factor(1:n)) ``` ## Author(s) Elvan Ceyhan

funsRankOrderTe function