runif.std.tetra {pcds}

Generation of Uniform Points in the Standard Regular Tetrahedron T_h

Description

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)).

Usage

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.

Value

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

Author(s)

Elvan Ceyhan

See Also

runif.tetra, runif.tri, and runif.multi.tri

Examples

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")