IarcCStri {pcds}

The indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs)

Description

Returns I(p2 is in N_{CS}(p1,t)) for points p1 and p2, that is, returns 1 if p2 is in NCS(p1,t), returns 0 otherwise, where N_{CS}(x,t) is the CS proximity region for point x with the expansion parameter t>0.

CS proximity region is constructed with respect to the triangle tri 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 or based on the circumcenter of tri. re is the index of the edge region p resides, with default=NULL

If p1 and p2 are distinct and either of them are outside tri, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

See also (Ceyhan (2005); Ceyhan et al. (2007); Ceyhan (2014)).

Usage

IarcCStri(p1, p2, tri, t, M, re = NULL)

Arguments

p1

A 2D point whose CS proximity region is constructed.

p2

A 2D point. The function determines whether p2 is inside the CS proximity region of p1 or not.

tri

A 3 \times 2 matrix with 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.

re

Index of the M-edge region containing the point p, either 1,2,3 or NULL (default is NULL).

Value

I(p2 is in NCS(p1,t)) for p1, that is, returns 1 if p2 is in NCS(p1,t), returns 0 otherwise

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2014). “Comparison of Relative Density of Two Random Geometric Digraph Families in Testing Spatial Clustering.” TEST, 23(1), 100-134.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

See Also

IarcAStri, IarcPEtri, IarcCStri, and IarcCSstd.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
tau<-1.5

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.2)

n<-10
set.seed(1)
Xp<-runif.tri(n,Tr)$g

IarcCStri(Xp[1,],Xp[2,],Tr,tau,M)

P1<-as.numeric(runif.tri(1,Tr)$g)
P2<-as.numeric(runif.tri(1,Tr)$g)
IarcCStri(P1,P2,Tr,tau,M)

#or try
re<-rel.edges.tri(P1,Tr,M)$re
IarcCStri(P1,P2,Tr,tau,M,re)