plotASarcs: The plot of the arcs of Arc Slice Proximity Catch Digraph...

In pcds: Proximity Catch Digraphs and Their Applications

The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case

Description

Plots the arcs of AS-PCD whose vertices are the data points in Xp and 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, arcs may exist for Xp points only inside the convex hull of Yp points. 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 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 arcs are only possible for points inside the convex hull of Yp points.

See (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds) for more on AS-PCDs. Also see (\insertCiteokabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

plotASarcs(
  Xp,
  Yp,
  M = "CC",
  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 AS-PCD.
Yp	A set of 2D points which constitute the vertices of the Delaunay triangulation. The Delaunay triangles partition the convex hull of Yp points.
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.
asp	A numeric value, giving the aspect ratio for y axis to x-axis 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 arcs 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

plotASarcs.tri, plotPEarcs.tri, plotPEarcs, plotCSarcs.tri, and plotCSarcs

Examples

#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-15; ny<-5;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

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))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))

M<-c(1,1,1)  #try also M<-c(1,2,3)

plotASarcs(Xp,Yp,M,asp=1,xlab="",ylab="")

plotASarcs(Xp,Yp[1:3,],M,asp=1,xlab="",ylab="")

pcds documentation built on May 29, 2024, 9:36 a.m.