pcds (version 0.1.4)

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

Description

Plots the arcs of PE-PCD whose vertices are the data points, Xp and the triangle tri. PE proximity regions are constructed with respect to the triangle tri with expansion parameter \(r \ge 1\), i.e., arcs may exist only for Xp points inside the triangle tri.

Vertex regions are based on center \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of the triangle tri or based on the circumcenter of tri; default is \(M=(1,1,1)\) i.e., the center of mass of tri.

See also (ceyhan:Phd-thesis,ceyhan:arc-density-PE,ceyhan:dom-num-NPE-Spat2011;textualpcds).

Usage

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

Value

A plot of the arcs of the PE-PCD whose vertices are the points in data set Xp and the triangle tri

Arguments

Xp

A set of 2D points which constitute the vertices of the PE-PCD.

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

r

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

M

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; default is \(M=(1,1,1)\) i.e., the center of mass 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.

Author

Elvan Ceyhan

References

See Also

plotPEarcsMT, plotASarcsTri and plotASarcsMT

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10  #try also n<-20

set.seed(1)
dat<-runif.tri(n,Tr)$g

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

r<-1.5  #try also r<-2

ifelse(isTRUE(all.equal(M,circ.cent.tri(Tr))),
Ds<-rbind((B+C)/2,(A+C)/2,(A+B)/2),Ds<-cp2e.tri(Tr,M))

dat<-matrix(dat,ncol=2)

Xlim<-range(Tr[,1],dat[,1],M[1])
Ylim<-range(Tr[,2],dat[,2],M[2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

if (dimension(M)==3) {M<-bary2cart(M,Tr)}
#need to run this when M is given in barycentric coordinates

plotPEarcsTri(dat,Tr,r,M,main="arcs of PE-PCD with r=1.5",
xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
if (dimension(M)==3) {M<-bary2cart(M,Tr)}
#need to run this when M is given in barycentric coordinates
L<-rbind(M,M,M); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)

txt<-rbind(Tr,M,Ds)
xc<-txt[,1]+c(-.02,.03,.03,.03,.05,-0.03,-.01)
yc<-txt[,2]+c(.02,.02,.02,.07,.02,.05,-.06)
txt.str<-c("A","B","C","M","D1","D2","D3")
text(xc,yc,txt.str)