| Idom.num1AStri {pcds} | R Documentation |
The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case
Description
Returns I(p is a dominating point of the AS-PCD whose vertices are the 2D data set Xp),
that is, returns 1 if p is a dominating point of AS-PCD, returns 0 otherwise.
Point, p, is in the region of vertex rv (default is NULL); vertices are labeled as 1,2,3
in the order they are stacked row-wise in tri.
AS proximity regions are defined with respect to the
triangle tri 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 circumcenter of tri;
default is M="CC", i.e., circumcenter of tri.
ch.data.pnt is for checking whether point p is a data point in Xp or not (default is FALSE),
so by default this function checks whether the point p would be a dominating point
if it actually were in the data set.
See also (Ceyhan (2005, 2010)).
Usage
Idom.num1AStri(p, Xp, tri, M = "CC", rv = NULL, ch.data.pnt = FALSE)
Arguments
p |
A 2D point that is to be tested for being a dominating point or not of the AS-PCD. |
Xp |
A set of 2D points which constitutes the vertices of the AS-PCD. |
tri |
Three 2D points, stacked row-wise, each row representing a vertex of the triangle. |
M |
The center of the triangle. |
rv |
Index of the vertex whose region contains point |
ch.data.pnt |
A logical argument for checking whether point |
Value
I(p is a dominating point of the AS-PCD whose vertices are the 2D data set Xp),
that is, returns 1 if p is a dominating point of the AS-PCD, returns 0 otherwise
Author(s)
Elvan Ceyhan
References
Ceyhan E (2005).
An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications.
Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.
Ceyhan E (2010).
“Extension of One-Dimensional Proximity Regions to Higher Dimensions.”
Computational Geometry: Theory and Applications, 43(9), 721-748.
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
Examples
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)$g
M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.2)
Idom.num1AStri(Xp[1,],Xp,Tr,M)
Idom.num1AStri(Xp[1,],Xp[1,],Tr,M)
Idom.num1AStri(c(1.5,1.5),c(1.6,1),Tr,M)
Idom.num1AStri(c(1.6,1),c(1.5,1.5),Tr,M)
gam.vec<-vector()
for (i in 1:n)
{gam.vec<-c(gam.vec,Idom.num1AStri(Xp[i,],Xp,Tr,M))}
ind.gam1<-which(gam.vec==1)
ind.gam1
#or try
Rv<-rel.vert.triCC(Xp[1,],Tr)$rv
Idom.num1AStri(Xp[1,],Xp,Tr,M,Rv)
Idom.num1AStri(c(.2,.4),Xp,Tr,M)
Idom.num1AStri(c(.2,.4),c(.2,.4),Tr,M)
Xp2<-rbind(Xp,c(.2,.4))
Idom.num1AStri(Xp[1,],Xp2,Tr,M)
if (dimension(M)==3) {M<-bary2cart(M,Tr)}
#need to run this when M is given in barycentric coordinates
CC<-circumcenter.tri(Tr) #the circumcenter
if (isTRUE(all.equal(M,CC)) || identical(M,"CC"))
{cent<-CC
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)
cent.name<-"CC"
} else
{cent<-M
cent.name<-"M"
Ds<-prj.cent2edges(Tr,M)
}
Xlim<-range(Tr[,1],Xp[,1])
Ylim<-range(Tr[,2],Xp[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
plot(A,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(Xp)
L<-rbind(cent,cent,cent); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(rbind(Xp[ind.gam1,]),pch=4,col=2)
txt<-rbind(Tr,cent,Ds)
xc<-txt[,1]
yc<-txt[,2]
txt.str<-c("A","B","C",cent.name,"D1","D2","D3")
text(xc,yc,txt.str)
Idom.num1AStri(c(1.5,1.1),Xp,Tr,M)
Idom.num1AStri(c(1.5,1.1),Xp,Tr,M)
Idom.num1AStri(c(1.5,1.1),Xp,Tr,M,ch.data.pnt=FALSE)
#gives an error message if ch.data.pnt=TRUE since point p is not a data point in Xp