Idom.setCSstd.tri {pcds} | R Documentation |
The indicator for the set of points S
being a dominating set or not for Central Similarity Proximity
Catch Digraphs (CS-PCDs) - standard equilateral triangle case
Description
Returns S
a dominating set of the CS-PCD where the vertices of the CS-PCD are the data set
Xp
), that is,
returns 1 if S
is a dominating set of CS-PCD, returns 0 otherwise.
CS proximity region is constructed
with respect to the standard equilateral triangle with
expansion parameter
and edge regions are based on the center
in Cartesian coordinates or
in barycentric coordinates in the interior of
;
default is
i.e., the center of mass of
(which is equivalent to the circumcenter of
).
Edges of ,
,
,
, are also labeled as 3, 1, and 2, respectively.
See also (Ceyhan (2012)).
Usage
Idom.setCSstd.tri(S, Xp, t, M = c(1, 1, 1))
Arguments
S |
A set of 2D points which is to be tested for being a dominating set for the CS-PCDs. |
Xp |
A set of 2D points which constitute the vertices of the CS-PCD. |
t |
A positive real number which serves as the expansion parameter in CS proximity region in the
standard equilateral triangle |
M |
A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates
which serves as a center in the interior of the standard equilateral triangle |
Value
S
a dominating set of the CS-PCD, that is, returns 1 if
S
is a dominating set of CS-PCD,
returns 0 otherwise, where CS proximity region is constructed in the standard equilateral triangle
Author(s)
Elvan Ceyhan
References
Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.
See Also
Idom.setCStri
and Idom.setPEstd.tri
Examples
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
n<-10
set.seed(1)
Xp<-runif.std.tri(n)$gen.points
M<-as.numeric(runif.std.tri(1)$g) #try also M<-c(.6,.2)
t<-.5
S<-rbind(Xp[1,],Xp[2,])
Idom.setCSstd.tri(S,Xp,t,M)
S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,])
Idom.setCSstd.tri(S,Xp,t,M)