pcds (version 0.1.2)

plotPEarcsMT: The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case

Description

Plots the arcs of 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 defined with respect to the Delaunay triangles based on Yp points with expansion parameter $r\ge 1$ and 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). Each Delaunay triangle is first converted to an (unscaled) basic triangle so that M will be the same type of center for each Delaunay triangle (this conversion is not necessary when M is $CM$).

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 (ceyhan:Phd-thesis,ceyhan:arc-density-PE,ceyhan:dom-num-NPE-Spat2011;textualpcds) for more on the PE-PCDs. Also see (okabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

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

Arguments

Xp

A set of 2D points which constitute the vertices 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.

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="").

xlab, ylab

Titles for the $x$ and $y$ axes, respectively (default="" 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 PE-PCD whose vertices are the points in data set Xp and the Delaunay triangles based on Yp points

References

See Also

plotPEarcsTri, plotASarcsMT, and plotCSarcsMT

Examples

# NOT RUN {
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-4;  #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,0,1),runif(ny,0,1))

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

r<-1.5  #try also r<-2

Xlim<-range(Xp[,1],Yp[,1])
Ylim<-range(Xp[,2],Yp[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plotPEarcsMT(Xp,Yp,r,M,xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))

plotPEarcsMT(Xp,Yp[1:3,],r,M,xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))

# }