plotPEregs.tetra {pcds}

The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - one tetrahedron case

Description

Plots the points in and outside of the tetrahedron th and also the PE proximity regions (which are also tetrahedrons) for points inside the tetrahedron th.

PE proximity regions are constructed with respect to tetrahedron th with expansion parameter r \ge 1 and vertex regions are based on the center M which is circumcenter ("CC") or center of mass ("CM") of th with default="CM", so PE proximity regions are defined only for points inside the tetrahedron th.

See also (Ceyhan (2005, 2010)).

Usage

plotPEregs.tetra(
  Xp,
  th,
  r,
  M = "CM",
  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.

th

A 4 \times 3 matrix with each row representing a vertex of the tetrahedron.

r

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

M

The center to be used in the construction of the vertex regions in the tetrahedron, th. Currently it only takes "CC" for circumcenter and "CM" for center of mass; default="CM".

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 tetrahedron th (and just the points outside th)

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.std.tetra, plotPEregs.tri and plotPEregs.int

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)
set.seed(1)
tetra<-rbind(A,B,C,D)+matrix(runif(12,-.25,.25),ncol=3) #adding jitter to make it non-regular

n<-5  #try also n<-20
Xp<-runif.tetra(n,tetra)$g  #try also Xp[,1]<-Xp[,1]+1

M<-"CM"  #try also M<-"CC"
r<-1.5

plotPEregs.tetra(Xp,tetra,r) #uses the default M="CM"
plotPEregs.tetra(Xp,tetra,r,M="CC")

plotPEregs.tetra(Xp[1,],tetra,r)  #uses the default M="CM"
plotPEregs.tetra(Xp[1,],tetra,r,M)