plotPEregs.std.tetra {pcds}

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 (2005, 2010)).

Usage

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

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.

Value

Plot of the PE proximity regions for points inside the standard regular tetrahedron T_h (and just the points outside T_h)

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

See Also

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

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)
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)