pcds (version 0.1.4)

cp2edges.nd: Projections of Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs) to its edges

Description

Returns the projections from center cent to the edges on the extension of the lines joining cent to the vertices in the triangle, tri. Here M is one of the three centers which gives nondegenerate asymptotic distribution of the domination number of PE-PCD for uniform data in tri for a given expansion parameter r in \((1,1.5]\). The center label cent values 1,2,3 correspond to the vertices \(M_1\), \(M_2\), and \(M_3\) (i.e., row numbers in the output of cent.nondeg(tri,r)); default for cent is 1. cent becomes center of mass \(CM\) for \(r=1.5\).

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

Usage

cp2edges.nd(tri, r, cent = 1)

Value

Three projection points (stacked row-wise) from one of the centers (as \(1,2,3\) corresponding to \(M_1,\,M_2,\,M_3\)) which gives nondegenerate asymptotic distribution of the domination number of PE-PCD for uniform data in tri for expansion parameter r in \((1,1.5]\).

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.

cent

Index of the center (as \(1,2,3\) corresponding to \(M_1,\,M_2,\,M_3\)) which gives nondegenerate asymptotic distribution of the domination number of PE-PCD for uniform data in tri for expansion parameter r in \((1,1.5]\); default cent=1.

Author

Elvan Ceyhan

References

See Also

cp2e.bastri and cp2e.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
r<-1.35

cp2edges.nd(Tr,r,cent=2)

Ms<-cent.nondeg(Tr,r)

Ds<-cp2edges.nd(Tr,r,cent=1)
D1<-Ds[1,]; D2<-Ds[2,]; D3<-Ds[3,]

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

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

points(Ds,pch=4,col=2)
L<-Tr; R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2,col=2)
txt<-Ds
xc<-txt[,1]
yc<-txt[,2]
txt.str<-c("D1","D2","D3")
text(xc,yc,txt.str)

cp2edges.nd(Tr,r,1)

dat.fr<-data.frame(a=Tr)
cp2edges.nd(dat.fr,r,1)

cp2edges.nd(Tr,r,cent=3)
#gives an error message if center index, cent, is different from 1, 2 or 3
cp2edges.nd(Tr,r=1.49,cent=2)
#gives an error message if r>1.5