pcds (version 0.1.4)

NumArcsCSTe: Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral 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 standard equilateral triangle \(T_e=T(v=1,v=2,v=3)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) 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 \(T_e\); default is \(M=(1,1,1)\) i.e., the center of mass of \(T_e\). For the number of arcs, loops are not allowed so arcs are only possible for points inside \(T_e\) for this function.

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

Usage

NumArcsCSTe(dat, t, M = c(1, 1, 1))

Value

Number of arcs for the CS-PCD with vertices being 2D data set, dat, in \(T_e\)

with expansion parameter, \(t>0\), and center of mass CM. CS proximity regions are defined only for dat points inside \(T_e\), i.e., arcs are possible for such points only.

Arguments

dat

A set of 2D points which constitute the vertices of the digraph.

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 standard equilateral triangle \(T_e\); default is \(M=(1,1,1)\) i.e. the center of mass of \(T_e\).

Author

Elvan Ceyhan

References

See Also

NumArcsCStri, NumArcsCSMT, and NumArcsPETe,

Examples

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
n<-10  #try also n<-20

set.seed(1)
dat<-runifTe(n)$gen.points

M<-as.numeric(runifTe(1)$g)  #try also M<-c(.6,.2)

NumArcsCSTe(dat,t=.5,M)
NumArcsCSTe(dat,t=3,M)
NumArcsCSTe(dat,t=1.5,M)

NumArcsCSTe(rbind(dat,c(0,1)),t=2,M)
NumArcsCSTe(c(.4,.2),t=.5,M)

NumArcsCSTe(dat,t=1.5,M);

NumArcsCSTe(rbind(dat,dat),t=1.5,M)

dat.fr<-data.frame(a=dat)
NumArcsCSTe(dat.fr,t=1.5,M);