pcds (version 0.1.8)

plotPEregs.std.tetra: The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - standard regular tetrahedron case

Description

Plots the points in and outside of the standard regular tetrahedron \(T_h=T((0,0,0),(1,0,0),(1/2,\sqrt{3}/2,0),(1/2,\sqrt{3}/6,\sqrt{6}/3))\) and also the PE proximity regions for points in data set Xp.

PE proximity regions are defined with respect to the standard regular tetrahedron \(T_h\) with expansion parameter \(r \ge 1\), so PE proximity regions are defined only for points inside \(T_h\).

Vertex regions are based on circumcenter (which is equivalent to the center of mass for the standard regular tetrahedron) of \(T_h\).

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010;textualpcds).

Usage

plotPEregs.std.tetra(
  Xp,
  r,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  zlab = NULL,
  xlim = NULL,
  ylim = NULL,
  zlim = NULL,
  ...
)

Value

Plot of the PE proximity regions for points inside the standard regular tetrahedron \(T_h\)

(and just the points outside \(T_h\))

Arguments

Xp

A set of 3D points for which PE proximity regions are constructed.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

main

An overall title for the plot (default=NULL).

xlab, ylab, zlab

titles for the \(x\), \(y\), and \(z\) axes, respectively (default=NULL for all).

xlim, ylim, zlim

Two numeric vectors of length 2, giving the \(x\)-, \(y\)-, and \(z\)-coordinate ranges (default=NULL for all).

...

Additional scatter3D parameters.

Author

Elvan Ceyhan

References

See Also

plotPEregs, plotASregs.tri, plotASregs, plotCSregs.tri, and plotCSregs

Examples

# \donttest{
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)
r<-1.5

n<-3  #try also n<-20
Xp<-runif.std.tetra(n)$g  #try also Xp[,1]<-Xp[,1]+1

plotPEregs.std.tetra(Xp[1:3,],r)

P1<-c(.1,.1,.1)
plotPEregs.std.tetra(rbind(P1,P1),r)
# }