# The closest points in a data set to edges in each $CM$-vertex region in a triangle An object of class `"Extrema"`. Returns the closest data points among the data set, `Xp`, to edge $j$ in $CM$-vertex region $j$ for $j=1,2,3$ in the triangle, `tri`$=T(A,B,C)$, where $CM$ stands for center of mass. Vertex labels are $A=1$, $B=2$, and $C=3$, and corresponding edge labels are $BC=1$, $AC=2$, and $AB=3$. Function yields `NA` if there are no data points in a $CM$-vertex region. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:masa-2007,ceyhan:comp-geo-2010,ceyhan:dom-num-NPE-Spat2011;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r cl2edgesCMvert.reg(Xp, tri) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. ## Returns A `list` with the elements - **txt1**: Vertex labels are $A=1$, $B=2$, and $C=3$ (correspond to row number in Extremum Points). - **txt2**: A short description of the distances as `"Distances to Edges in the Respective CM-Vertex Regions"`. - **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, here, closest points to edges in the respective vertex region. - **X**: The input data, `Xp`, 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, here, it is `tri` - **cent**: The center point used for construction of vertex regions - **ncent**: Name of the center, `cent`, it is `"CM"` for this function - **regions**: Vertex regions inside the triangle, `tri`, provided as a `list` - **region.names**: Names of the vertex regions as `"vr=1"`, `"vr=2"`, and `"vr=3"` - **region.centers**: Centers of mass of the vertex regions inside `tri` - **dist2ref**: Distances of closest points in the vertex regions to corresponding edges ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); n<-20 #try also n<-100 set.seed(1) Xp<-runif.tri(n,Tr)$g Ext<-cl2edgesCMvert.reg(Xp,Tr) Ext summary(Ext) plot(Ext) cl2e<-Ext CM<-(A+B+C)/3; D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; Ds<-rbind(D1,D2,D3) Xlim<-range(Tr[,1],Xp[,1]) Ylim<-range(Tr[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Tr,pch=".",xlab="",ylab="", main="Closest Points in CM-Vertex Regions \n to the Opposite Edges", axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) xc<-Tr[,1]+c(-.02,.02,.02) yc<-Tr[,2]+c(.02,.02,.04) txt.str<-c("A","B","C") text(xc,yc,txt.str) points(Xp,pch=1,col=1) L<-matrix(rep(CM,3),ncol=2,byrow=TRUE); R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty=2) points(cl2e$ext,pch=3,col=2) txt<-rbind(CM,Ds) xc<-txt[,1]+c(-.04,.04,-.03,0) yc<-txt[,2]+c(-.05,.04,.06,-.08) txt.str<-c("CM","D1","D2","D3") 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`, `cl2edgesCCvert.reg`, `cl2edgesMvert.reg`, and `cl2edges.std.tri` ## Author(s) Elvan Ceyhan

cl2edgesCMvert.reg function