IarcCStri.alt: An alternative to the function 'IarcCStri' which yields the...

In pcds: Proximity Catch Digraphs and Their Applications

An alternative to the function IarcCStri which yields 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 N_{CS}(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 of mass, CM. re is the index of the CM-edge region p resides, with default=NULL but must be provided as vertices (y_1,y_2,y_3) for re=3 as rbind(y2,y3,y1) for re=1 and as rbind(y1,y3,y2) for re=2 for triangle T(y_1,y_2,y_3).

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 (\insertCiteceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

IarcCStri.alt(p1, p2, tri, t, 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.
re	Index of the CM-edge region containing the point p, either 1,2,3 or NULL, default=NULL but must be provided (row-wise) as vertices (y_1,y_2,y_3) for re=3 as (y_2,y_3,y_1) for re=1 and as (y_1,y_3,y_2) for re=2 for triangle T(y_1,y_2,y_3).

Value

I(p2 is in N_{CS}(p1,t)) for p1, that is, returns 1 if p2 is in N_{CS}(p1,t), returns 0 otherwise.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

IarcAStri, IarcPEtri, IarcCStri, and IarcCSstd.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.6,2);
Tr<-rbind(A,B,C);
t<-1.5

P1<-c(.4,.2)
P2<-c(1.8,.5)
IarcCStri(P1,P2,Tr,t,M=c(1,1,1))
IarcCStri.alt(P1,P2,Tr,t)

IarcCStri(P2,P1,Tr,t,M=c(1,1,1))
IarcCStri.alt(P2,P1,Tr,t)

#or try
re<-rel.edges.triCM(P1,Tr)$re
IarcCStri(P1,P2,Tr,t,M=c(1,1,1),re)
IarcCStri.alt(P1,P2,Tr,t,re)

pcds documentation built on May 29, 2024, 9:36 a.m.