# Functions provide the indices of the Delaunay triangles where the points reside Two functions: `index.delaunay.tri` and `indices.delaunay.tri`. `index.delaunay.tri` finds the index of the Delaunay triangle in which the given point, `p`, resides. `indices.delaunay.tri` finds the indices of triangles for all the points in data set, `Xp`, as a vector. Delaunay triangulation is based on `Yp` and `DTmesh` are the Delaunay triangles with default `NULL`. The function returns `NA` for a point not inside the convex hull of `Yp`. Number of `Yp` points (i.e., size of `Yp`) should be at least three and the points should be in general position so that Delaunay triangulation is (uniquely) defined. If the number of `Yp` points is 3, then there is only one Delaunay triangle and the indices of all the points inside this triangle are all 1. See (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="okabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textual",package="pcds",cached_env=.Rdpack.currefs) ) for more on Delaunay triangulation and the corresponding algorithm. ```r index.delaunay.tri(p, Yp, DTmesh = NULL) indices.delaunay.tri(Xp, Yp, DTmesh = NULL) ``` ## Arguments - `p`: A 2D point; the index of the Delaunay triangle in which `p` resides is to be determined. It is an argument for `index.delaunay.tri`. - `Yp`: A set of 2D points from which Delaunay triangulation is constructed. - `DTmesh`: Delaunay triangles based on `Yp`, default is `NULL`, which is computed via `tri.mesh` function in `interp` package. `triangles` function yields a triangulation data structure from the triangulation object created by `tri.mesh`. - `Xp`: A set of 2D points representing the set of data points for which the indices of the Delaunay triangles they reside is to be determined. It is an argument for `indices.delaunay.tri`. ## Returns `index.delaunay.tri` returns the index of the Delaunay triangle in which the given point, `p`, resides and `indices.delaunay.tri` returns the `vector` of indices of the Delaunay triangles in which points in the data set, `Xp`, reside. ## Examples ```r #Examples for index.delaunay.tri nx<-20 #number of X points (target) ny<-5 #number of Y points (nontarget) set.seed(1) Yp<-cbind(runif(ny),runif(ny)) Xp<-runif.multi.tri(nx,Yp)$g #data under CSR in the convex hull of Ypoints #try also Xp<-cbind(runif(nx),runif(nx)) index.delaunay.tri(Xp[10,],Yp) #or use DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove") #Delaunay triangulation TRY<-interp::triangles(DTY)[,1:3]; index.delaunay.tri(Xp[10,],Yp,DTY) ind.DT<-vector() for (i in 1:nx) ind.DT<-c(ind.DT,index.delaunay.tri(Xp[i,],Yp)) ind.DT Xlim<-range(Yp[,1],Xp[,1]) Ylim<-range(Yp[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove") #Delaunay triangulation based on Y points #plot of the data in the convex hull of Y points together with the Delaunay triangulation plot(Xp,main=" ", xlab=" ", ylab=" ",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05),type="n") interp::plot.triSht(DTY, add=TRUE, do.points = TRUE,pch=16,col="blue") points(Xp,pch=".",cex=3) text(Xp,labels = factor(ind.DT)) #Examples for indices.delaunay.tri #nx is number of X points (target) and ny is number of Y points (nontarget) nx<-20; ny<-4; #try also nx<-40; ny<-10 or nx<-1000; ny<-10; set.seed(1) Yp<-cbind(runif(ny),runif(ny)) Xp<-runif.multi.tri(nx,Yp)$g #data under CSR in the convex hull of Ypoints #try also Xp<-cbind(runif(nx),runif(nx)) tr.ind<-indices.delaunay.tri(Xp,Yp) #indices of the Delaunay triangles tr.ind #or use DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove") #Delaunay triangulation based on Y points tr.ind<-indices.delaunay.tri(Xp,Yp,DTY) #indices of the Delaunay triangles tr.ind Xlim<-range(Yp[,1],Xp[,1]) Ylim<-range(Yp[,2],Xp[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] #plot of the data in the convex hull of Y points together with the Delaunay triangulation oldpar <- par(pty = "s") plot(Xp,main=" ", xlab=" ", ylab=" ",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05),pch=".") interp::plot.triSht(DTY, add=TRUE, do.points = TRUE,pch=16,col="blue") text(Xp,labels = factor(tr.ind)) par(oldpar) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## Author(s) Elvan Ceyhan

funsIndDelTri function