plotASregs.tri {pcds}

The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - one triangle case

Description

Plots the points in and outside of the triangle tri and also the AS proximity regions for points in data set Xp.

AS proximity regions are defined with respect to the triangle tri, so AS proximity regions are defined only for points inside the triangle tri and vertex regions are based on the 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 circumcenter of tri; default is M="CC", i.e., circumcenter of tri. When vertex regions are constructed with 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.

See also (Ceyhan (2005, 2010)).

Usage

plotASregs.tri(
  Xp,
  tri,
  M = "CC",
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  vert.reg = FALSE,
  ...
)

Arguments

Xp

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

tri

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

M

The center of the triangle. "CC" stands for circumcenter of the triangle tri or a 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle T_b; default is M="CC" i.e., the circumcenter of tri.

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).

vert.reg

A logical argument to add vertex regions to the plot, default is vert.reg=FALSE.

...

Additional plot parameters.

Value

Plot of the AS proximity regions for points inside the triangle tri (and only the points outside tri)

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.

See Also

plotASregs, plotPEregs.tri, plotPEregs, plotCSregs.tri, and plotCSregs

Examples

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

set.seed(1)
Xp0<-runif.tri(n,Tr)$g
M<-as.numeric(runif.tri(1,Tr)$g)  #try also  #M<-c(1.6,1.2);

plotASregs.tri(Xp0,Tr,M,main="Proximity Regions for AS-PCD", xlab="",ylab="")
Xp = Xp0[1,]
plotASregs.tri(Xp,Tr,M,main="Proximity Regions for AS-PCD", xlab="",ylab="")

#can plot the arcs of the AS-PCD
#plotASarcs.tri(Xp,Tr,M,main="Arcs of AS-PCD",xlab="",ylab="")

plotASregs.tri(Xp,Tr,M,main="Proximity Regions for AS-PCD", xlab="",ylab="",vert.reg=TRUE)

# or try the default center
#plotASregs.tri(Xp,Tr,main="Proximity Regions for AS-PCD", xlab="",ylab="",vert.reg=TRUE);
M = (arcsAStri(Xp,Tr)$param)$c #the part "M = as.numeric(arcsAStri(Xp,Tr)$param)" is optional,
#for the below annotation of the plot

#can add vertex labels and text to the figure (with vertex regions)
#but first we need to determine whether the center used for vertex regions is CC or not
#see the description for more detail.
CC<-circumcenter.tri(Tr)
#Arcs<-arcsAStri(Xp,Tr,M)
#M = as.numeric(Arcs$parameters)
if (isTRUE(all.equal(M,CC)) || identical(M,"CC"))
{cent<-CC
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)
cent.name<-"CC"
} else
{cent<-M
cent.name<-"M"
Ds<-prj.cent2edges(Tr,M)
}

#now we add the vertex names and annotation
txt<-rbind(Tr,cent,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",cent.name,"D1","D2","D3")
text(xc,yc,txt.str)