# Generation of Uniform Points in the first one-sixth of standard equilateral triangle An object of class `"Uniform"`. Generates `n` points uniformly in the first 1/6th of the standard equilateral triangle $T_e=(A,B,C)$ with vertices with $A=(0,0)$; $B=(1,0)$, $C=(1/2,\sqrt{3}/2)$ (see the examples below). The first 1/6th of the standard equilateral triangle is the triangle with vertices $A=(0,0)$, $(1/2,0)$, $C=(1/2,\sqrt{3}/6)$. ```r runif.std.tri.onesixth(n) ``` ## Arguments - `n`: a positive integer representing number of uniform points to be generated in the first one-sixth of $T_e$. ## Returns A `list` with the elements - **type**: The type of the point pattern - **mtitle**: The `"main"` title for the plot of the point pattern - **support**: The vertices of the support of the uniformly generated points - **gen.points**: The output set of uniformly generated points in the first 1/6th of the standard equilateral triangle. - **out.region**: The outer region for the one-sixth of $T_e$, which is just $T_e$ here. - **desc.pat**: Description of the point pattern - **num.points**: The `vector` of two numbers, which are the number of generated points and the number of vertices of the support (i.e., `Y`) points. - **txt4pnts**: Description of the two numbers in `num.points`. - **xlimit,ylimit**: The ranges of the $x$- and $y$-coordinates of the generated, support and outer region points ## Examples ```r A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C); CM<-(A+B+C)/3; D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; Ds<-rbind(D1,D2,D3) nx<-100 #try also nx<-1000 #data generation step set.seed(1) Xdt<-runif.std.tri.onesixth(nx) Xdt summary(Xdt) plot(Xdt,asp=1) Xd<-Xdt$gen.points #plot of the data with the regions in the equilateral triangle Xlim<-range(Te[,1]) Ylim<-range(Te[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Te,asp=1,pch=".",xlim=Xlim+xd*c(-.01,.01), ylim=Ylim+yd*c(-.01,.01),xlab=" ",ylab=" ", main="first 1/6th of the \n standard equilateral triangle") polygon(Te) L<-Te; R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty=2) polygon(rbind(A,D3,CM),col=5) points(Xd) #letter annotation of the plot txt<-rbind(A,B,C,CM,D1,D2,D3) xc<-txt[,1]+c(-.02,.02,.02,.04,.05,-.03,0) yc<-txt[,2]+c(.02,.02,.02,.03,0,.03,-.03) txt.str<-c("A","B","C","CM","D1","D2","D3") text(xc,yc,txt.str) ``` ## See Also `runif.std.tri`, `runif.basic.tri`, `runif.tri`, and `runif.multi.tri` ## Author(s) Elvan Ceyhan

runif.std.tri.onesixth function