plotPEregsMT: The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - multiple triangle case

Description

Plots the points in and outside of the Delaunay triangles based on Yp points which partition the convex hull of Yp points and also plots the PE proximity regions for Xp points and the Delaunay triangles based on Yp points.

PE proximity regions are constructed with respect to the Delaunay triangles with the expansion parameter $r \geq 1$ .

Vertex regions in each triangle is based on the center $M = (α, β, γ)$ 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).

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

Usage

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

Arguments

A set of 2D points for which PE proximity regions are constructed.

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

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

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri or the circumcenter of tri.

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

Plot of the Xp points, Delaunay triangles based on Yp points and also the PE proximity regions for Xp points inside the convex hull of Yp points

References

Examples

Run this code

# 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))

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

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

r<-1.5  #try also r<-2

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

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

# }

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