num.arcsCStri {pcds} | R Documentation |
Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the triangle - one triangle case
Description
An object of class "NumArcs"
.
Returns the number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs)
whose vertices are the
given 2D numerical data set, Xp
.
It also provides number of vertices
(i.e., number of data points inside the triangle)
and indices of the data points that reside in the triangle.
CS proximity region is defined with respect to the triangle,
tri
with expansion parameter
and edge regions are based on the center
in Cartesian coordinates or
in barycentric coordinates in the interior of
tri
;
default is i.e., the center of mass of
tri
.
For the number of arcs, loops are not allowed so
arcs are only possible for points inside tri
for this function.
See also (Ceyhan (2005); Ceyhan et al. (2007); Ceyhan (2014)).
Usage
num.arcsCStri(Xp, tri, t, M = c(1, 1, 1))
Arguments
Xp |
A set of 2D points which constitute the vertices of CS-PCD. |
tri |
A |
t |
A positive real number which serves as the expansion parameter in CS proximity region. |
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
desc |
A short description of the output: number of arcs and quantities related to the triangle |
num.arcs |
Number of arcs of the CS-PCD |
tri.num.arcs |
Number of arcs of the induced subdigraph of the CS-PCD
for vertices in the triangle |
num.in.tri |
Number of |
ind.in.tri |
The vector of indices of the |
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 |
vertices |
Vertices of the digraph, |
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 (2014).
“Comparison of Relative Density of Two Random Geometric Digraph Families in Testing Spatial Clustering.”
TEST, 23(1), 100-134.
Ceyhan E, Priebe CE, Marchette DJ (2007).
“A new family of random graphs for testing spatial segregation.”
Canadian Journal of Statistics, 35(1), 27-50.
See Also
num.arcsCSstd.tri
, num.arcsCS
, num.arcsPEtri
,
and num.arcsAStri
Examples
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10 #try also n<-20
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)
Narcs = num.arcsCStri(Xp,Tr,t=.5,M)
Narcs
summary(Narcs)
plot(Narcs)