| Idom.num2CS.Te.onesixth {pcds} | R Documentation |
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 (Ceyhan (2005)).
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 |
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
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.