| IarcCS.Te.onesixth {pcds} | R Documentation |
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 |
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