Idom.num2CS.Te.onesixth: The indicator for two points constituting a dominating set...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

The indicator for two points constituting a dominating set for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one-sixth of the standard equilateral triangle case

Description

Returns I({p1,p2} is a dominating set of the CS-PCD) where the vertices of the CS-PCD are the 2D data set Xp), that is, returns 1 if p is a dominating point of CS-PCD, returns 0 otherwise.

CS proximity region is constructed with respect to the standard equilateral triangle T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2)) and with expansion parameter t=1. Point, p1, must lie in the first one-sixth of T_e, which is the triangle with vertices T(A,D_3,CM)=T((0,0),(1/2,0),CM).

ch.data.pnts is for checking whether points p1 and p2 are data points in Xp or not (default is FALSE), so by default this function checks whether the points p1 and p2 would be a dominating set if they actually were in the data set.

See also (\insertCiteceyhan:Phd-thesis;textualpcds).

Usage

Idom.num2CS.Te.onesixth(p1, p2, Xp, ch.data.pnts = FALSE)

Arguments

p1, p2	Two 2D points to be tested for constituting a dominating set of the CS-PCD.
Xp	A set of 2D points which constitutes the vertices of the CS-PCD.
ch.data.pnts	A logical argument for checking whether points p1 and p2 are data points in Xp or not (default is FALSE).

Value

I({p1,p2} is a dominating set of the CS-PCD) where the vertices of the CS-PCD are the 2D data set Xp), that is, returns 1 if {p1,p2} is a dominating set of CS-PCD, returns 0 otherwise

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

Idom.num2CSstd.tri

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.