plotPEedges {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 - multiple 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 in Xp in the multiple triangle case and the Delaunay triangles based on Yp points.

PE proximity regions are constructed with respect to the Delaunay triangles based on Yp points, i.e., PE proximity regions are defined only for Xp points inside the convex hull of Yp points. That is, edges may exist for Xp points only inside the convex hull of Yp points.

Vertex regions in each triangle are based on the center M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of each Delaunay triangle or based on circumcenter of each Delaunay triangle (default for M=(1,1,1) which is the center of mass of the triangle).

Convex hull of Yp is partitioned by the Delaunay triangles based on Yp points (i.e., multiple triangles are the set of these Delaunay triangles whose union constitutes the convex hull of Yp points). Loops are not allowed so edges are only possible for points inside the convex hull of Yp points.

See (Ceyhan (2005, 2016)) for more on the PE-PCDs. Also, see (Okabe et al. (2000); Ceyhan (2010); Sinclair (2016)) for more on Delaunay triangulation and the corresponding algorithm.

Usage

plotPEedges(
  Xp,
  Yp,
  r,
  M = c(1, 1, 1),
  ugraph = c("underlying", "reflexivity"),
  asp = NA,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

Arguments

Xp

A set of 2D points which constitute the vertices of the underlying or reflexivity graphs of the PE-PCD.

Yp

A set of 2D points which constitute the vertices of the Delaunay triangles.

r

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

M

A 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle or circumcenter of each Delaunay triangle (for this, argument should be set as M="CC"), default for M=(1,1,1) which is the center of mass of each triangle.

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).

...

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 Delaunay triangles based on Yp points

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 (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

Ceyhan E (2016). “Edge Density of New Graph Types Based on a Random Digraph Family.” Statistical Methodology, 33, 31-54.

Okabe A, Boots B, Sugihara K, Chiu SN (2000). Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley, New York.

Sinclair D (2016). “S-hull: a fast radial sweep-hull routine for Delaunay triangulation.” 1604.01428.

See Also

plotPEedges.tri, plotASedges, plotCSedges, and plotPEarcs

Examples

#\donttest{
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-5;

set.seed(1)
Xp<-cbind(runif(nx,0,1),runif(nx,0,1))
Yp<-cbind(runif(ny,0,.25),
runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1))

M<-c(1,1,1)
r<-1.5

plotPEedges(Xp,Yp,r,M,xlab="",ylab="")
plotPEedges(Xp,Yp,r,M,xlab="",ylab="",ugraph="r")
#}