pcds (version 0.1.4)

ArcsPEtri: The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - one triangle case

Description

An object of class "PCDs". Returns arcs as tails (or sources) and heads (or arrow ends) for data set Xp as the vertices of PE-PCD.

PE proximity regions are constructed with respect to the triangle tri with expansion parameter \(r \ge 1\), i.e., arcs may exist for points only inside tri. It also provides various descriptions and quantities about the arcs of the PE-PCD such as number of arcs, arc density, etc.

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;textualpcds).

Usage

ArcsPEtri(Xp, tri, r, M = c(1, 1, 1))

Value

A list with the elements

type

A description of the type of the digraph

parameters

Parameters of the digraph, here, it is the center used to construct the vertex regions.

tess.points

Points on which the tessellation of the study region is performed, here, tessellation is the support triangle.

tess.name

Name of data set used in tessellation (i.e., vertices of the triangle)

vertices

Vertices of the digraph, Xp points

vert.name

Name of the data set which constitute the vertices of the digraph

S

Tails (or sources) of the arcs of PE-PCD for 2D data set Xp as vertices of the digraph

E

Heads (or arrow ends) of the arcs of PE-PCD for 2D data set Xp as vertices of the digraph

mtitle

Text for "main" title in the plot of the digraph

quant

Various quantities for the digraph: number of vertices, number of partition points, number of intervals, number of arcs, and arc density.

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.

Author

Elvan Ceyhan

References

See Also

ArcsPEMT, ArcsAStri and ArcsCStri

Examples

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

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

ArcsPEtri(dat,Tr,r,M)

Arcs<-ArcsPEtri(dat,Tr,r,M)
Arcs
summary(Arcs)
plot(Arcs)

S<-Arcs$S
E<-Arcs$E

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]

Ds<-cp2e.tri(Tr,M)

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

plot(Tr,pch=".",xlab="",ylab="",axes=TRUE,
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(dat,pch=1,col=1)
L<-rbind(M,M,M); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
arrows(S[,1], S[,2], E[,1], E[,2], length = 0.1, col= 4)

txt<-rbind(Tr,M,Ds)
xc<-txt[,1]+c(-.02,.03,.02,.03,.04,-.03,-.01)
yc<-txt[,2]+c(.02,.02,.03,.06,.04,.05,-.07)
txt.str<-c("A","B","C","M","D1","D2","D3")
text(xc,yc,txt.str)

r<-2
ArcsPEtri(dat,Tr,r,M)

dat.fr<-data.frame(a=dat)
ArcsPEtri(dat.fr,Tr,r,M)

dat.fr<-data.frame(a=Tr)
ArcsPEtri(dat,dat.fr,r,M)