pcds (version 0.1.2)

NumArcsCStri: Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

Description

Returns the number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) whose vertices are the given 2D numerical data set, dat.

CS proximity region \(N_{CS}(x,t)\) is defined with respect to the triangle, tri with expansion parameter \(t>0\) and edge 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 tri; default is \(M=(1,1,1)\) i.e., the center of mass of tri. For the number of arcs, loops are not allowed so arcs are only possible for points inside tri for this function.

See also (ceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

NumArcsCStri(Dt, tri, t, M = c(1, 1, 1))

Arguments

Dt

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

tri

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

t

A positive real number which serves as the expansion parameter in CS proximity region.

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

Value

Number of arcs for the CS-PCD with vertices being 2D data set, dat, in tri with expansion parameter, \(t>0\), and center of mass CM. CS proximity regions are defined only for Dt points inside tri, i.e., arcs are possible for such points only.

References

See Also

NumArcsCSTe, NumArcsCSMT, NumArcsPEtri, and NumArcsAStri

Examples

# NOT RUN {
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)

NumArcsCStri(dat,Tr,t=.5,M)
NumArcsCStri(dat,Tr,t=1,M)
NumArcsCStri(dat,Tr,t=1.5,M)

NumArcsCStri(c(1.4,.2),Tr,t=.5,M)

t<-.5
NumArcsCStri(dat,Tr,t,M)

dat.fr<-data.frame(a=dat)
NumArcsCStri(dat.fr,Tr,t,M)

dat.fr<-data.frame(a=Tr)
NumArcsCStri(dat,dat.fr,t,M)

# }