pcds (version 0.1.6)

NumArcsPEtri: Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one 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, Xp. It also provides number of vertices (i.e., number of data points inside the triangle) and indices of the data points that reside in the triangle.

PE proximity region \(N_{PE}(x,r)\) is defined with respect to the triangle, tri for this function. PE proximity region is constructed 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 the triangle tri or based on circumcenter 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 the triangle tri for this function.

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

Usage

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

Value

A list with the elements

num.arcs

Number of arcs of the PE-PCD

num.in.tri

Number of Xp points in the triangle, tri

ind.in.tri

The vector of indices of the Xp points that reside in the triangle

Arguments

Xp

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

tri

A \(3 \times 2\) matrix with 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 which may be entered as "CC" as well; default is \(M=(1,1,1)\) i.e., the center of mass of tri.

Author

Elvan Ceyhan

References

See Also

NumArcsPETe, NumArcsPE, NumArcsCStri, and NumArcsAStri

Examples

if (FALSE) {
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)
Xp<-runif.tri(n,Tr)$g

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

NumArcsPEtri(Xp,Tr,r=1.25,M)
NumArcsPEtri(Xp,Tr,r=1.5,M)
}