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<table width="100%" summary="page for IarcCSt1.std.tri"><tr><td>IarcCSt1.std.tri</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch
Digraphs (CS-PCDs) - standard equilateral triangle case with <i>t=1</i></h2>

<h3>Description</h3>

<p>Returns <i>I(</i><code>p2</code> is in <i>N_{CS}(p1,t=1))</i> for points <code>p1</code> and <code>p2</code>, that is, returns 1 if <code>p2</code> is in <i>N_{CS}(p1,t=1)</i>,
returns 0 otherwise, where <i>N_{CS}(x,t=1)</i> is the CS proximity region for point <i>x</i> with expansion parameter <i>t=1</i>.
</p>
<p>CS proximity region is defined with respect to the standard equilateral triangle
<i>T_e=T(A,B,C)=T((0,0),(1,0),(1/2,&radic;{3}/2))</i> and edge regions are based on the center of mass <i>CM=(1/2,&radic;{3}/6)</i>.
</p>
<p>If <code>p1</code> and <code>p2</code> are distinct and either are outside <i>T_e</i>, it returns 0,
but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).
</p>


<h3>Usage</h3>

<pre>
IarcCSt1.std.tri(p1, p2)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>p1</code></td>
<td>
<p>A 2D point whose CS proximity region is constructed.</p>
</td></tr>
<tr valign="top"><td><code>p2</code></td>
<td>
<p>A 2D point. The function determines whether <code>p2</code> is inside the CS proximity region of
<code>p1</code> or not.</p>
</td></tr>
</table>


<h3>Value</h3>

<p><i>I(</i><code>p2</code> is in <i>N_{CS}(p1,t=1))</i> for <code>p1</code> in <i>T_e</i> that is, returns 1 if <code>p2</code>
is in <i>N_{CS}(p1,t=1)</i>, returns 0 otherwise
</p>


<h3>Author(s)</h3>

<p>Elvan Ceyhan
</p>


<h3>See Also</h3>

<p><code>IarcCSstd.tri</code>
</p>


<h3>Examples</h3>

<pre>

A&lt;-c(0,0); B&lt;-c(1,0); C&lt;-c(1/2,sqrt(3)/2);
Te&lt;-rbind(A,B,C);
n&lt;-3

set.seed(1)
Xp&lt;-runif.std.tri(n)$gen.points

IarcCSt1.std.tri(Xp[1,],Xp[2,])
IarcCSt1.std.tri(c(.2,.5),Xp[2,])


</pre>


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