plotASedges.tri {pcds.ugraph}

The plot of the edges of the underlying or reflexivity graph of the Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - one triangle case

Description

Plots the edges of the underlying or reflexivity graph of the Arc Slice Proximity Catch Digraph (AS-PCD) whose vertices are the data points, Xp and also the triangle tri. AS proximity regions are constructed with respect to the triangle tri, only for Xp points inside the triangle tri. i.e., edges may exist only for Xp points inside the triangle tri.

Vertex regions are based on the 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 circumcenter of tri; default is M="CC", i.e., circumcenter 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.

See also (Ceyhan (2005, 2016)).

Usage

plotASedges.tri(
  Xp,
  tri,
  M = "CC",
  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 AS-PCD.

tri

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

M

The center of the triangle. "CC" stands for circumcenter of the triangle tri or a 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle T_b; default is M="CC", i.e., the circumcenter of tri.

ugraph

The type of the graph based on AS-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 AS-PCD whose vertices are the points in data set Xp and also the triangle tri

A plot of the edges of the underlying or reflexivity graphs of the AS-PCD whose vertices are the points in data set Xp where AS proximity regions are defined with respect to the triangle tri; also plots 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

plotASedges, plotPEedges.tri, plotCSedges.tri, and plotASarcs.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)
plotASedges.tri(Xp,Tr,M,vert.reg = TRUE,xlab="",ylab="")
plotASedges.tri(Xp,Tr,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)
#}