IndCS.Te.onesixth

A 2D point whose CS proximity region is constructed.

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

Returns \(I(\)<code>pt2</code> is in \(N_{CS}(pt1,t=1))\) for points <code>pt1</code> and <code>pt2</code>,
that is, returns 1 if <code>pt2</code> 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 <code>pt1</code> 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 <code>pt1</code> and <code>pt2</code> are distinct and <code>pt1</code> is outside of \(T(A,D_3,CM)\) or <code>pt2</code> 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).

Contains the functions for generating patterns of segregation, association, complete spatial randomness (CSR))
and Uniform data in one, two and three dimensional cases, for testing these patterns based on two invariants of
various families of the proximity catch digraphs (PCDs) (see (Ceyhan (2005) ISBN:978-3-639-19063-2).
The graph invariants used in testing spatial point data are the domination number (Ceyhan (2011)
<doi:10.1080/03610921003597211>) and arc density (Ceyhan et al. (2006) <doi:10.1016/j.csda.2005.03.002>;
Ceyhan et al. (2007) <doi:10.1002/cjs.5550350106>) of for two-dimensional data for visualization of PCDs for one,
two and three dimensional data. The PCD families considered are Arc-Slice PCDs,
Proportional-Edge PCDs and Central Similarity PCDs.

Elvan Ceyhan

pcds

Proximity Catch Digraphs and Their Applications

IndCS.Te.onesixth function

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 — 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

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

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See Also