pcds (version 0.1.8)

Idom.setPEtri: The indicator for the set of points S being a dominating set or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

Description

Returns \(I(\)S a dominating set of PE-PCD whose vertices are the data set Xp\()\), that is, returns 1 if S is a dominating set of PE-PCD, and returns 0 otherwise.

PE proximity region is constructed with respect to the triangle tri with the expansion parameter \(r \ge 1\) and vertex regions are based on the center \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of the triangle tri or based on the circumcenter of tri; default is \(M=(1,1,1)\), i.e., the center of mass of tri. The triangle tri\(=T(A,B,C)\) has edges \(AB\), \(BC\), \(AC\) which are also labeled as edges 3, 1, and 2, respectively.

See also (ceyhan:Phd-thesis,ceyhan:masa-2007,ceyhan:dom-num-NPE-Spat2011,ceyhan:mcap2012;textualpcds).

Usage

Idom.setPEtri(S, Xp, tri, r, M = c(1, 1, 1))

Value

\(I(\)S a dominating set of PE-PCD\()\), that is, returns 1 if S is a dominating set of PE-PCD whose vertices are the data points in Xp; and returns 0 otherwise, where PE proximity region is constructed in the triangle tri.

Arguments

S

A set of 2D points which is to be tested for being a dominating set for the PE-PCDs.

Xp

A set of 2D points which constitute the vertices of the PE-PCD.

tri

A \(3 \times 2\) matrix with each row representing a vertex of the triangle.

r

A positive real number which serves as the expansion parameter in PE proximity region constructed in the triangle tri; must be \(\ge 1\).

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri or the circumcenter of tri which may be entered as "CC" as well; default is \(M=(1,1,1)\), i.e., the center of mass of tri.

Author

Elvan Ceyhan

References

See Also

Idom.setPEstd.tri, IarcPEset2pnt.tri, Idom.setCStri, and Idom.setAStri

Examples

# \donttest{
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

set.seed(1)
Xp<-runif.tri(n,Tr)$gen.points

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

r<-1.5

S<-rbind(Xp[1,],Xp[2,])
Idom.setPEtri(S,Xp,Tr,r,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,])
Idom.setPEtri(S,Xp,Tr,r,M)

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
Idom.setPEtri(S,Xp,Tr,r,M)
# }