plotASarcs.tri {pcds}

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

Description

Plots the arcs of AS-PCD whose vertices are the data points, Xp and also the triangle tri. AS proximity regions are constructed with respect to the triangle tri, i.e., only for Xp points inside the triangle tri. If there are duplicates of Xp points, only one point is retained for each duplicate value, and a warning message is printed.

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 the center is the 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

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

Arguments

Xp

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

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.

asp

A numeric value, giving the aspect ratio for y axis to x-axis 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).

vert.reg

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

...

Additional plot parameters.

Value

A plot of the arcs of the AS-PCD for a 2D data set Xp where AS proximity regions are defined with respect to the triangle tri; also plots the triangle 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

plotASarcs, plotPEarcs.tri, plotPEarcs, plotCSarcs.tri, and plotCSarcs

Examples

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

set.seed(1)
Xp<-runif.tri(n,Tr)$g  #try also Xp<-cbind(runif(n,1,2),runif(n,0,2))

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

plotASarcs.tri(Xp,Tr,M,main="Arcs of AS-PCD",xlab="",ylab="")

plotASarcs.tri(Xp,Tr,M,main="Arcs of AS-PCD",xlab="",ylab="",vert.reg = TRUE)

# or try the default center
#plotASarcs.tri(Xp,Tr,asp=1,main="arcs of 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)

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,.02,.02,.01,.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)