pcds (version 0.1.4)

NumArcsPETe: Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

Description

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

PE proximity region \(N_{PE}(x,r)\) 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 \(r \ge 1\) and 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 \(T_e\); 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:arc-density-PE;textualpcds).

Usage

NumArcsPETe(dat, r, M = c(1, 1, 1))

Value

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

with expansion parameter, \(r \ge 1\), and M-vertex regions. PE 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 PE-PCD.

r

A positive real number which serves as the expansion parameter for 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 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

NumArcsPEtri, NumArcsPEMT, and NumArcsCSTe

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<-c(.6,.2)  #try also M<-c(1,1,1)

NumArcsPETe(dat,r=1.25,M)
NumArcsPETe(dat,r=1.5,M)
NumArcsPETe(dat,r=2,M)

NumArcsPETe(rbind(dat,c(0,1)),r=2,M)
NumArcsPETe(c(.2,.3),r=2,M)

NumArcsPETe(dat,r=1.5,M);

dat.fr<-data.frame(a=dat)
NumArcsPETe(dat.fr,r=1.5,M);