pcds (version 0.1.4)

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))

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.

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.

Author

Elvan Ceyhan

References

See Also

NumArcsCSTe, NumArcsCSMT, NumArcsPEtri, and NumArcsAStri

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)

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)