pcds (version 0.1.8)

IarcCStri.alt: 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 (ceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

IarcCStri.alt(p1, p2, tri, t, re = NULL)

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.

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 \(T(y_1,y_2,y_3)\).

Author

Elvan Ceyhan

References

See Also

IarcAStri, IarcPEtri, IarcCStri, and IarcCSstd.tri

Examples

# \donttest{
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)
# }