pcds (version 0.1.2)

cent.nondeg: Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs)

Description

Returns the centers which yield nondegenerate asymptotic distribution for the domination number of PE-PCD for uniform data in a triangle, tri\(=T(v_1,v_2,v_3)\).

PE proximity region is defined with respect to the triangle tri with expansion parameter r in \((1,1.5]\).

Vertex regions are defined with the centers that are output of this function. Centers are stacked row-wise with row number is corresponding to the vertex row number in tri (see the examples for an illustration). The center labels 1,2,3 correspond to the vertices \(M_1\), \(M_2\), and \(M_3\) (which are the three centers for r in \((1,1.5)\) which becomes center of mass for \(r=1.5\).).

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

Usage

cent.nondeg(tri, r)

Arguments

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be in \((1,1.5]\) for this function.

Value

The centers (stacked row-wise) which give nondegenerate asymptotic distribution for the domination number of PE-PCD for uniform data in a triangle, tri.

References

Examples

# NOT RUN {
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
r<-1.35

Ms<-cent.nondeg(Tr,r)
Ms

Xlim<-range(Tr[,1])
Ylim<-range(Tr[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Tr,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(Ms,pch=".",col=1)
polygon(Ms,lty=2)

xc<-Tr[,1]+c(-.02,.02,.02)
yc<-Tr[,2]+c(.02,.02,.03)
txt.str<-c("A","B","C")
text(xc,yc,txt.str)

xc<-Ms[,1]+c(-.04,.04,.03)
yc<-Ms[,2]+c(.02,.02,.05)
txt.str<-c("M1","M2","M3")
text(xc,yc,txt.str)

cent.nondeg(Tr,r)

dat.fr<-data.frame(a=Tr)
cent.nondeg(dat.fr,r)

# }