runif.std.tetra: Generation of Uniform Points in the Standard Regular...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

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

## Not run: 
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)

## End(Not run)

## Not run: 
#need to install scatterplot3d package and call "library(scatterplot3d)"
s3d<-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")

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.