plotASedges: The plot of the edges of the underlying or reflexivity graph...

In pcds.ugraph: Underlying Graphs of Proximity Catch Digraphs and Their Applications

The plot of the edges of the underlying or reflexivity graph of the Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - multiple 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 in Xp in the multiple triangle case and the Delaunay triangles based on Yp points.

AS proximity regions are constructed with respect to the Delaunay triangles based on Yp points, i.e., AS 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 are based on the center M="CC" for circumcenter of each Delaunay triangle or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of each Delaunay triangle; default is M="CC", i.e., circumcenter of each triangle. 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.

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 (\insertCiteceyhan:Phd-thesis,ceyhan:stamet2016;textualpcds.ugraph) for more on the AS-PCDs. Also, see (\insertCiteokabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds.ugraph) for more on Delaunay triangulation and the corresponding algorithm.

Usage

plotASedges(
  Xp,
  Yp,
  M = "CC",
  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 AS-PCD.
Yp	A set of 2D points which constitute the vertices of the Delaunay triangles.
M	The center of the triangle. "CC" stands for circumcenter of each Delaunay triangle or 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle; default is M="CC", i.e., the circumcenter of each triangle.
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).
...	Additional plot parameters.

Value

A plot of the edges of the underlying or reflexivity graphs of the AS-PCD for a 2D data set Xp where AS proximity regions are defined with respect to the Delaunay triangles based on Yp points; also plots the Delaunay triangles based on Yp points.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

plotASedges.tri, plotPEedges, plotCSedges, and plotASarcs

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)

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

pcds.ugraph documentation built on May 29, 2024, 10:39 a.m.