plotPEedges.tri {pcds.ugraph}

The plot of the edges of the underlying or reflexivity graph of the Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - one triangle case

Description

Plots the edges of the underlying or reflexivity graph of the Proportional Edge Proximity Catch Digraph (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., edges may exist only for Xp points inside the triangle tri.

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 edge density and domination number the PE-PCDs based on uniform data.

See also (Ceyhan (2005, 2016)).

Usage

plotPEedges.tri(
  Xp,
  tri,
  r,
  M = c(1, 1, 1),
  ugraph = c("underlying", "reflexivity"),
  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 underlying or reflexivity graphs 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.

ugraph

The type of the graph based on PE-PCDs, "underlying" is for the underlying graph, and "reflexivity" is for the reflexivity graph (default is "underlying").

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 edges of the underlying or reflexivity graphs 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 (2016). “Edge Density of New Graph Types Based on a Random Digraph Family.” Statistical Methodology, 33, 31-54.

See Also

plotPEedges, plotASedges.tri, plotCSedges.tri, and plotPEarcs.tri

Examples

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

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

M<-as.numeric(pcds::runif.tri(1,Tr)$g)
r<-1.5
plotPEedges.tri(Xp,Tr,r,M,vert.reg = TRUE,xlab="",ylab="")
plotPEedges.tri(Xp,Tr,r,M,ugraph="r",vert.reg = TRUE,xlab="",ylab="")

#can add vertex labels and text to the figure (with vertex regions)
ifelse(isTRUE(all.equal(M,pcds::circumcenter.tri(Tr))),
{Ds<-rbind((B+C)/2,(A+C)/2,(A+B)/2); cent.name="CC"},
{Ds<-pcds::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)
#}