PEarc.dens.tri | R Documentation |
Returns the arc density of PE-PCD
whose vertex set is the given 2D numerical data set, Xp
,
(some of its members are) in the triangle tri
.
PE proximity regions is defined with respect to tri
with
expansion parameter r \ge 1
and vertex regions are
based on 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=(1,1,1)
, i.e.,
the center of mass of tri
.
The function also provides arc density standardized
by the mean and asymptotic variance of the arc density
of PE-PCD for uniform data in the triangle tri
only when M
is the center of mass.
For the number of arcs, loops are not allowed.
tri.cor
is a logical argument for triangle correction
(default is TRUE
),
if TRUE
, only the points
inside the triangle are considered
(i.e., digraph induced by these vertices are considered) in computing
the arc density, otherwise all points are considered
(for the number of vertices in the denominator of arc density).
See also (\insertCiteceyhan:Phd-thesis,ceyhan:arc-density-PE;textualpcds).
PEarc.dens.tri(Xp, tri, r, M = c(1, 1, 1), tri.cor = FALSE)
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 |
tri.cor |
A logical argument
for computing the arc density for only the points inside the triangle,
|
A list
with the elements
arc.dens |
Arc density of PE-PCD
whose vertices are the 2D numerical data set, |
std.arc.dens |
Arc density standardized
by the mean and asymptotic variance of the arc
density of PE-PCD for uniform data in the triangle |
Elvan Ceyhan
ASarc.dens.tri
, CSarc.dens.tri
,
and num.arcsPEtri
## Not run:
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)
num.arcsPEtri(Xp,Tr,r=1.5,M)
PEarc.dens.tri(Xp,Tr,r=1.5,M)
PEarc.dens.tri(Xp,Tr,r=1.5,M,tri.cor = TRUE)
## End(Not run)
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