plotCSregs.tri {pcds}

The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - one triangle case

Description

Plots the points in and outside of the triangle tri and also the CS proximity regions which are also triangular for points inside the triangle tri with edge regions are based on the center of mass CM.

CS proximity regions are defined with respect to the triangle tri with expansion parameter t>0, so CS proximity regions are defined only for points inside the triangle tri.

Edge regions are based on center M=(m_1,m_2) in Cartesian coordinates or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of the triangle tri; default is M=(1,1,1) i.e., the center of mass of tri.

See also (Ceyhan (2005); Ceyhan et al. (2007); Ceyhan (2014)).

Usage

plotCSregs.tri(
  Xp,
  tri,
  t,
  M = c(1, 1, 1),
  asp = NA,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  edge.reg = FALSE,
  ...
)

Arguments

Xp

A set of 2D points for which CS proximity regions are constructed.

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

t

A positive real number which serves as the expansion parameter in CS proximity region.

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri; default is M=(1,1,1) i.e., the center of mass of tri.

asp

A numeric value, giving the aspect ratio y/x (default is NA), see the official help page for asp by typing "? asp".

main

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

xlab, ylab

Titles for the x and y axes, respectively (default=NULL for both).

xlim, ylim

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

edge.reg

A logical argument to add edge regions to the plot, default is edge.reg=FALSE.

...

Additional plot parameters.

Value

Plot of the CS proximity regions for points inside the triangle tri (and just the points outside tri)

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 (2014). “Comparison of Relative Density of Two Random Geometric Digraph Families in Testing Spatial Clustering.” TEST, 23(1), 100-134.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

See Also

plotCSregs, plotASregs.tri and plotPEregs.tri,

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

set.seed(1)
Xp0<-runif.tri(n,Tr)$g
M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

t<-.5  #try also t<-2

plotCSregs.tri(Xp0,Tr,t,M,main="Proximity Regions for CS-PCD", xlab="",ylab="")

Xp = Xp0[1,]
plotCSregs.tri(Xp,Tr,t,M,main="CS Proximity Regions with t=.5", xlab="",ylab="",edge.reg=TRUE)

# or try the default center
plotCSregs.tri(Xp,Tr,t,main="CS Proximity Regions with t=.5", xlab="",ylab="",edge.reg=TRUE);
#M=(arcsCStri(Xp,Tr,r)$param)$c #the part "M=(arcsPEtri(Xp,Tr,r)$param)$cent" is optional,
#for the below annotation of the plot

#can add vertex labels and text to the figure (with edge regions)
txt<-rbind(Tr,M)
xc<-txt[,1]+c(-.02,.02,.02,.02)
yc<-txt[,2]+c(.02,.02,.02,.03)
txt.str<-c("A","B","C","M")
text(xc,yc,txt.str)