# The closest points in a data set to edges in the standard equilateral triangle An object of class `"Extrema"`. Returns the closest points from the 2D data set, `Xp`, to the edges in the standard equilateral triangle $T_e=T(A=(0,0),B=(1,0),C=(1/2,\sqrt{3}/2))$. `ch.all.intri` is for checking whether all data points are inside $T_e$ (default is `FALSE`). If some of the data points are not inside $T_e$ and `ch.all.intri=TRUE`, then the function yields an error message. If some of the data points are not inside $T_e$ and `ch.all.intri=FALSE`, then the function yields the closest points to edges among the data points inside $T_e$ (yields `NA` if there are no data points inside $T_e$). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:arc-density-PE,ceyhan:masa-2007;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r cl2edges.std.tri(Xp, ch.all.intri = FALSE) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points. - `ch.all.intri`: A logical argument (default=`FALSE`) to check whether all data points are inside the standard equilateral triangle $T_e$. So, if it is `TRUE`, the function checks if all data points are inside the closure of the triangle (i.e., interior and boundary combined) else it does not. ## Returns A `list` with the elements - **txt1**: Edge labels as $AB=3$, $BC=1$, and $AC=2$ for $T_e$ (correspond to row number in Extremum Points). - **txt2**: A short description of the distances as `"Distances to Edges ..."`. - **type**: Type of the extrema points - **desc**: A short description of the extrema points - **mtitle**: The `"main"` title for the plot of the extrema - **ext**: The extrema points, i.e., closest points to edges - **X**: The input data, `Xp`, which can be a `matrix` or `data frame` - **num.points**: The number of data points, i.e., size of `Xp` - **supp**: Support of the data points, i.e., the standard equilateral triangle $T_e$ - **cent**: The center point used for construction of edge regions, not required for this extrema, hence it is `NULL` for this function - **ncent**: Name of the center, `cent`, not required for this extrema, hence it is `NULL` for this function - **regions**: Edge regions inside the triangle, $T_e$, not required for this extrema, hence it is `NULL` for this function - **region.names**: Names of the edge regions, not required for this extrema, hence it is `NULL` for this function - **region.centers**: Centers of mass of the edge regions inside $T_e$, not required for this extrema, hence it is `NULL` for this function - **dist2ref**: Distances from closest points in each edge region to the corresponding edge ## Examples ```r n<-20 #try also n<-100 Xp<-runif.std.tri(n)$gen.points Ext<-cl2edges.std.tri(Xp) Ext summary(Ext) plot(Ext,asp=1) ed.clo<-Ext A<-c(0,0); B<-c(1,0); C<-c(0.5,sqrt(3)/2); Te<-rbind(A,B,C) CM<-(A+B+C)/3 p1<-(A+B)/2 p2<-(B+C)/2 p3<-(A+C)/2 Xlim<-range(Te[,1],Xp[,1]) Ylim<-range(Te[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(A,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05), ylim=Ylim+yd*c(-.05,.05)) polygon(Te) points(Xp,xlab="",ylab="") points(ed.clo$ext,pty=2,pch=4,col="red") txt<-rbind(Te,p1,p2,p3) xc<-txt[,1]+c(-.03,.03,.03,0,0,0) yc<-txt[,2]+c(.02,.02,.02,0,0,0) txt.str<-c("A","B","C","re=1","re=2","re=3") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `cl2edges.vert.reg.basic.tri`, `cl2edgesMvert.reg`, `cl2edgesCMvert.reg` and `fr2edgesCMedge.reg.std.tri` ## Author(s) Elvan Ceyhan

cl2edges.std.tri function