Idom.num1CS.Te.onesixth: 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:Phd-thesis;textualpcds).

Usage

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

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).

Author

Elvan Ceyhan