# Generation of Uniform Points in the Convex Hull of Points An object of class `"Uniform"`. Generates `n` points uniformly in the Convex Hull of set of points, `Yp`. That is, generates uniformly in each of the triangles in the Delaunay triangulation of `Yp`, i.e., in the multiple triangles partitioning the convex hull of `Yp`. If `Yp` consists only of 3 points, then the function behaves like the function `runif.tri`. `DTmesh` is the Delaunay triangulation of `Yp`, default is `DTmesh=NULL`. `DTmesh` yields triangulation nodes with neighbours (result of `tri.mesh` function from `interp` package). 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 runif.multi.tri(n, Yp, DTmesh = NULL) ``` ## Arguments - `n`: A positive integer representing the number of uniform points to be generated in the convex hull of the point set `Yp`. - `Yp`: A set of 2D points whose convex hull is the support of the uniform points to be generated. - `DTmesh`: Triangulation nodes with neighbours (result of `tri.mesh` function from `interp` package). ## Returns A `list` with the elements - **type**: The type of the pattern from which points are to be generated - **mtitle**: The `"main"` title for the plot of the point pattern - **tess.points**: The points which constitute the vertices of the triangulation and whose convex hull determines the support of the generated points. - **gen.points**: The output set of generated points uniformly in the convex hull of `Yp` - **out.region**: The outer region which contains the support region, `NULL` for this function. - **desc.pat**: Description of the point pattern from which points are to be generated - **num.points**: The `vector` of two numbers, which are the number of generated points and the number of vertices in the triangulation (i.e., size of `Yp`) points. - **txt4pnts**: Description of the two numbers in `num.points` - **xlimit,ylimit**: The ranges of the $x$- and $y$-coordinates of the points in Yp ## Examples ```r #nx is number of X points (target) and ny is number of Y points (nontarget) nx<-100; ny<-4; #try also nx<-1000; ny<-10; set.seed(1) Yp<-cbind(runif(ny,0,10),runif(ny,0,10)) Xdt<-runif.multi.tri(nx,Yp) #data under CSR in the convex hull of Ypoints Xdt summary(Xdt) plot(Xdt) Xp<-Xdt$g #or use DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove") #Delaunay triangulation based on Y points Xp<-runif.multi.tri(nx,Yp,DTY)$g #data under CSR in the convex hull of Ypoints Xlim<-range(Yp[,1]) Ylim<-range(Yp[,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 plot(Xp, xlab=" ", ylab=" ", main="Uniform Points in Convex Hull of Y Points", 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) Yp<-rbind(c(.3,.2),c(.4,.5),c(.14,.15)) runif.multi.tri(nx,Yp) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `runif.tri`, `runif.std.tri`, and `runif.basic.tri`, ## Author(s) Elvan Ceyhan

runif.multi.tri function