IarcCS.Te.onesixth: The indicator for the presence of an arc from a point to...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one-sixth of the standard equilateral triangle case

Description

Returns I(p2 is in N_{CS}(p1,t=1)) for points p1 and p2, that is, returns 1 if p2 is in N_{CS}(p1,t=1), returns 0 otherwise, where N_{CS}(x,t=1) is the CS proximity region for point x with expansion parameter t=1.

CS proximity region is defined with respect to the standard equilateral triangle T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2)) and edge regions are based on the center of mass CM=(1/2,\sqrt{3}/6). Here 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). If p1 and p2 are distinct and p1 is outside of T(A,D_3,CM) or p2 is outside T_e, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

Usage

IarcCS.Te.onesixth(p1, p2)

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.

Value

I(p2 is in N_{CS}(p1,t=1)) for p1 in the first one-sixth of T_e, T(A,D_3,CM), that is, returns 1 if p2 is in N_{CS}(p1,t=1), returns 0 otherwise

Author(s)

Elvan Ceyhan

See Also

IarcCSstd.tri

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