arcsPEtri {pcds} | R Documentation |
The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - one triangle case
Description
An object of class "PCDs"
.
Returns arcs of PE-PCD as tails (or sources) and heads (or arrow ends)
and related parameters and the quantities of the digraph.
The vertices of the PE-PCD are the data points in Xp
in the one triangle case.
PE proximity regions are constructed
with respect to the triangle tri
with expansion
parameter , i.e.,
arcs may exist only for points inside
tri
.
It also provides various descriptions
and quantities about the arcs of the PE-PCD
such as number of arcs, arc density, etc.
Vertex regions are based on center
in Cartesian coordinates or
in barycentric coordinates in the interior of
the triangle
tri
or based on the circumcenter of tri
;
default is , i.e., the center of mass of
tri
.
When the center is the circumcenter, CC
,
the vertex regions are constructed based on the
orthogonal projections to the edges,
while with any interior center M
,
the vertex regions are constructed using the extensions
of the lines combining vertices with M
.
M
-vertex regions are recommended spatial inference,
due to geometry invariance property of the arc density
and domination number the PE-PCDs based on uniform data.
See also (Ceyhan (2005); Ceyhan et al. (2006)).
Usage
arcsPEtri(Xp, tri, r, M = c(1, 1, 1))
Arguments
Xp |
A set of 2D points which constitute the vertices of the PE-PCD. |
tri |
A |
r |
A positive real number
which serves as the expansion parameter in PE proximity region;
must be |
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 |
Value
A list
with the elements
type |
A description of the type of the digraph |
parameters |
Parameters of the digraph,
the center |
tess.points |
Tessellation points, i.e., points on which the tessellation of
the study region is performed,
here, tessellation points are the vertices of the support triangle |
tess.name |
Name of the tessellation points |
vertices |
Vertices of the digraph, |
vert.name |
Name of the data set which constitutes the vertices of the digraph |
S |
Tails (or sources) of the arcs of PE-PCD
for 2D data set |
E |
Heads (or arrow ends) of the arcs of PE-PCD
for 2D data set |
mtitle |
Text for |
quant |
Various quantities for the digraph: number of vertices, number of partition points, number of triangles, number of arcs, and arc density. |
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, Priebe CE, Wierman JC (2006).
“Relative density of the random -factor proximity catch digraphs for testing spatial patterns of segregation and association.”
Computational Statistics & Data Analysis, 50(8), 1925-1964.
See Also
arcsPE
, arcsAStri
,
and arcsCStri
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(1.6,1.0)
r<-1.5 #try also r<-2
Arcs<-arcsPEtri(Xp,Tr,r,M)
#or try with the default center Arcs<-arcsPEtri(Xp,Tr,r); M= (Arcs$param)$cent
Arcs
summary(Arcs)
plot(Arcs)
#can add vertex regions
#but we first need to determine center is the circumcenter or not,
#see the description for more detail.
CC<-circumcenter.tri(Tr)
if (isTRUE(all.equal(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)
}
L<-rbind(cent,cent,cent); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
#now we can add the vertex names and annotation
txt<-rbind(Tr,cent,Ds)
xc<-txt[,1]+c(-.02,.02,.02,.02,.03,-.03,-.01)
yc<-txt[,2]+c(.02,.02,.03,.06,.04,.05,-.07)
txt.str<-c("A","B","C","M","D1","D2","D3")
text(xc,yc,txt.str)