pcds (version 0.1.4)

IndCS.Te.onesixth: 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 $I($pt2 is in $N_{CS}(pt1,t=1))$ for points pt1 and pt2, that is, returns 1 if pt2 is in $N_{CS}(pt1,t=1)$, 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 pt1 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 pt1 and pt2 are distinct and pt1 is outside of $T(A,D_3,CM)$ or pt2 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

IndCS.Te.onesixth(pt1, pt2)

Value

$I($pt2 is in $N_{CS}(pt1,t=1))$ for pt1 in the first one-sixth of $T_e$, $T(A,D_3,CM)$, that is, returns 1 if pt2 is in $N_{CS}(pt1,t=1)$, returns 0 otherwise

Arguments

pt1

A 2D point whose CS proximity region is constructed.

pt2

A 2D point. The function determines whether pt2 is inside the CS proximity region of pt1 or not.

Author

Elvan Ceyhan

See Also

IndCSTe