rel.verts.triCM {pcds} | R Documentation |
The indices of the CM
-vertex regions in a triangle
that contains the points in a give data set
Description
Returns the indices of the vertices
whose regions contain the points in data set Xp
in
a triangle tri
=(A,B,C)
and vertex regions are based on the center of mass CM
of tri
.
(see the plots in the example for illustrations).
The vertices of the triangle tri
are labeled as
1=A
, 2=B
, and 3=C
also
according to the row number the vertex is recorded in tri
.
If a point in Xp
is not inside tri
,
then the function yields NA
as output for that entry.
The corresponding vertex region is the polygon
with the vertex, CM
,
and midpoints the edges crossing the vertex.
See also (Ceyhan (2005, 2010)).
Usage
rel.verts.triCM(Xp, tri)
Arguments
Xp |
A set of 2D points representing the set of data points for which indices of the vertex regions containing them are to be determined. |
tri |
A |
Value
A list
with two elements
rv |
Indices (i.e., a |
tri |
The vertices of the triangle,
where row number corresponds to the vertex index in |
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
rel.verts.tri
, rel.verts.triCC
,
and rel.verts.tri.nondegPE
Examples
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
P<-c(.4,.2)
rel.verts.triCM(P,Tr)
n<-20 #try also n<-40
set.seed(1)
Xp<-runif.tri(n,Tr)$g
rv<-rel.verts.triCM(Xp,Tr)
rv
CM<-(A+B+C)/3
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)
Xlim<-range(Tr[,1],Xp[,1])
Ylim<-range(Tr[,2],Xp[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
plot(Tr,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(Xp,pch=".",col=1)
L<-matrix(rep(CM,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)
xc<-Tr[,1]+c(-.04,.05,.05)
yc<-Tr[,2]+c(-.05,.05,.03)
txt.str<-c("rv=1","rv=2","rv=3")
text(xc,yc,txt.str)
txt<-rbind(CM,Ds)
xc<-txt[,1]+c(.04,.04,-.03,0)
yc<-txt[,2]+c(-.07,.04,.06,-.08)
txt.str<-c("CM","D1","D2","D3")
text(xc,yc,txt.str)
text(Xp,labels=factor(rv$rv))