Idom.num1CS.Te.onesixth {pcds}

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

Description

Returns I(p is a dominating point of the 2D data set Xp of CS-PCD) in the standard equilateral triangle T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2)), that is, returns 1 if p is a dominating point of CS-PCD, returns 0 otherwise.

Point, p, 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).

CS proximity region is constructed with respect to T_e with expansion parameter t=1.

ch.data.pnt is for checking whether point p is a data point in Xp or not (default is FALSE), so by default this function checks whether the point p would be a dominating point if it actually were in the data set.

See also (Ceyhan (2005)).

Usage

Idom.num1CS.Te.onesixth(p, Xp, ch.data.pnt = FALSE)

Arguments

p

A 2D point that is to be tested for being a dominating point or not of the CS-PCD.

Xp

A set of 2D points which constitutes the vertices of the CS-PCD.

ch.data.pnt

A logical argument for checking whether point p is a data point in Xp or not (default is FALSE).

Value

I(p is a dominating point 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, 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.

See Also

Idom.num1CSstd.tri and Idom.num1CSt1std.tri