plotCSarcs.tri {pcds}

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

Description

Plots the arcs of CS-PCD whose vertices are the data points, Xp and the triangle tri. CS proximity regions are constructed with respect to the triangle tri with expansion parameter t>0, i.e., arcs may exist only for Xp points inside the triangle tri. If there are duplicates of Xp points, only one point is retained for each duplicate value, and a warning message is printed.

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

plotCSarcs.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 which constitute the vertices of the CS-PCD.

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

A plot of the arcs of the CS-PCD whose vertices are the points in data set Xp and the triangle 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

plotCSarcs, plotPEarcs.tri and plotASarcs.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10  #try also n<-20

set.seed(1)
Xp<-runif.tri(n,Tr)$g

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

t<-1.5  #try also t<-2

plotCSarcs.tri(Xp,Tr,t,M,main="Arcs of CS-PCD with t=1.5",
xlab="",ylab="",edge.reg = TRUE)

# or try the default center
#plotCSarcs.tri(Xp,Tr,t,main="Arcs of CS-PCD with t=1.5",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,.03)
yc<-txt[,2]+c(.02,.02,.02,.03)
txt.str<-c("A","B","C","M")
text(xc,yc,txt.str)