plotPEarcs.tri {pcds}

The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - one triangle case

Description

Plots the arcs of PE-PCD whose vertices are the data points, Xp and the triangle tri. PE proximity regions are constructed with respect to the triangle tri with expansion parameter r \ge 1, 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.

Vertex 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 or based on the circumcenter of tri; default is M=(1,1,1), i.e., the center of mass of tri. When the center is the circumcenter, CC, the vertex regions are constructed based on the orthogonal projections to the edges, while with any interior center M, the vertex regions are constructed using the extensions of the lines combining vertices with M. M-vertex regions are recommended spatial inference, due to geometry invariance property of the arc density and domination number the PE-PCDs based on uniform data.

See also (Ceyhan (2005); Ceyhan et al. (2006); Ceyhan (2011)).

Usage

plotPEarcs.tri(
  Xp,
  tri,
  r,
  M = c(1, 1, 1),
  asp = NA,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  vert.reg = FALSE,
  ...
)

Arguments

Xp

A set of 2D points which constitute the vertices of the PE-PCD.

tri

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

r

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

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 or the circumcenter of tri which may be entered as "CC" as well; 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).

vert.reg

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

...

Additional plot parameters.

Value

A plot of the arcs of the PE-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 (2011). “Spatial Clustering Tests Based on Domination Number of a New Random Digraph Family.” Communications in Statistics - Theory and Methods, 40(8), 1363-1395.

Ceyhan E, Priebe CE, Wierman JC (2006). “Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.” Computational Statistics & Data Analysis, 50(8), 1925-1964.

See Also

plotASarcs.tri, plotCSarcs.tri, and plotPEarcs

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) or M<-circumcenter.tri(Tr)
r<-1.5  #try also r<-2
plotPEarcs.tri(Xp,Tr,r,M,main="Arcs of PE-PCD with r = 1.5",
xlab="",ylab="",vert.reg = TRUE)

# or try the default center
#plotPEarcs.tri(Xp,Tr,r,main="Arcs of PE-PCD with r = 1.5",
#xlab="",ylab="",vert.reg = TRUE);
#M=(arcsPEtri(Xp,Tr,r)$param)$cent
#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 vertex regions)
ifelse(isTRUE(all.equal(M,circumcenter.tri(Tr))),
{Ds<-rbind((B+C)/2,(A+C)/2,(A+B)/2); cent.name="CC"},
{Ds<-prj.cent2edges(Tr,M); cent.name="M"})

txt<-rbind(Tr,M,Ds)
xc<-txt[,1]+c(-.02,.02,.02,.02,.04,-0.03,-.01)
yc<-txt[,2]+c(.02,.02,.02,.07,.02,.04,-.06)
txt.str<-c("A","B","C",cent.name,"D1","D2","D3")
text(xc,yc,txt.str)