# Generation of Uniform Points in the Standard Regular Tetrahedron $T_h$ An object of class `"Uniform"`. Generates `n` points uniformly in the standard regular tetrahedron $T_h=T((0,0,0),(1,0,0),(1/2,\sqrt{3}/2,0),(1/2,\sqrt{3}/6,\sqrt{6}/3))$. ```r runif.std.tetra(n) ``` ## Arguments - `n`: A positive integer representing the number of uniform points to be generated in the standard regular tetrahedron $T_h$. ## 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 vertices of the support region of the uniformly generated points, it is the standard regular tetrahedron $T_h$ for this function - **gen.points**: The output set of generated points uniformly in the standard regular tetrahedron $T_h$. - **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 of the support points (here it is 4). - **txt4pnts**: Description of the two numbers in `num.points` - **xlimit,ylimit,zlimit**: The ranges of the $x$-, $y$-, and $z$-coordinates of the support, $T_h$ ## Examples ```r A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0); D<-c(1/2,sqrt(3)/6,sqrt(6)/3) tetra<-rbind(A,B,C,D) n<-100 set.seed(1) Xdt<-runif.std.tetra(n) Xdt summary(Xdt) plot(Xdt) Xp<-runif.std.tetra(n)$g Xlim<-range(tetra[,1]) Ylim<-range(tetra[,2]) Zlim<-range(tetra[,3]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] zd<-Zlim[2]-Zlim[1] plot3D::scatter3D(Xp[,1],Xp[,2],Xp[,3], phi =20,theta=15, bty = "g", pch = 20, cex = 1, ticktype = "detailed", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05), zlim=Zlim+zd*c(-.05,.05)) #add the vertices of the tetrahedron plot3D::points3D(tetra[,1],tetra[,2],tetra[,3], add=TRUE) L<-rbind(A,A,A,B,B,C); R<-rbind(B,C,D,C,D,D) plot3D::segments3D(L[,1], L[,2], L[,3], R[,1], R[,2],R[,3], add=TRUE,lwd=2) plot3D::text3D(tetra[,1]+c(.05,0,0,0),tetra[,2],tetra[,3], labels=c("A","B","C","D"), add=TRUE) s3d<-scatterplot3d::scatterplot3d(Xp, highlight.3d=TRUE,xlab="x", ylab="y",zlab="z", col.axis="blue", col.grid="lightblue", main="3D Scatterplot of the data", pch=20) s3d$points3d(tetra,pch=20,col="blue") ``` ## See Also `runif.tetra`, `runif.tri`, and `runif.multi.tri` ## Author(s) Elvan Ceyhan

runif.std.tetra function