plotCSarcs: The plot of the arcs of Central Similarity Proximity Catch...

In pcds: Proximity Catch Digraphs and Their Applications

The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - multiple triangle case

Description

Plots the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) whose vertices are the data points in Xp in the multiple triangle case and the Delaunay triangles based on Yp points. If there are duplicates of Xp points, only one point is retained for each duplicate value, and a warning message is printed.

CS proximity regions are defined with respect to the Delaunay triangles based on Yp points with expansion parameter t>0 and edge regions in each triangle are based on the center M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior 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 arcs are only possible for points inside the convex hull of Yp points.

See (\insertCiteceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds) more on the CS-PCDs. Also see (\insertCiteokabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

plotCSarcs(
  Xp,
  Yp,
  t,
  M = c(1, 1, 1),
  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 CS-PCD.
Yp	A set of 2D points which constitute the vertices of the Delaunay triangles.
t	A positive real number which serves as the expansion parameter in CS proximity region.
M	A 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle, default for M=(1,1,1) which is the center of mass of each triangle.
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 arcs of the CS-PCD whose vertices are the points in data set Xp and the Delaunay triangles based on Yp points

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

plotCSarcs.tri, plotASarcs, and plotPEarcs

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)
t<-1.5  #try also t<-2

plotCSarcs(Xp,Yp,t,M,xlab="",ylab="")

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