PEarc.dens.tetra {pcds} | R Documentation |
Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Description
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 tetrahedron th
.
PE proximity region is constructed with respect to the tetrahedron th
and
vertex regions are based on the center M
which is circumcenter ("CC"
) or
center of mass ("CM"
) of th
with default="CM"
.
For the number of arcs, loops are not
allowed so arcs are only possible for points inside the tetrahedron th
for this function.
th.cor
is a logical argument for tetrahedron correction (default is TRUE
), if TRUE
, only the points
inside the tetrahedron 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 (Ceyhan (2005, 2010)).
Usage
PEarc.dens.tetra(Xp, th, r, M = "CM", th.cor = FALSE)
Arguments
Xp |
A set of 2D points which constitute the vertices of the PE-PCD. |
th |
A |
r |
A positive real number which serves as the expansion parameter in PE proximity region;
must be |
M |
The center to be used in the construction of the vertex regions in the tetrahedron, |
th.cor |
A logical argument for computing the arc density for only the points inside the tetrahedron,
|
Value
Arc density of PE-PCD whose vertices are the 2D numerical data set, Xp
;
PE proximity regions are defined with respect to the tetrahedron th
and M
-vertex regions
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.
See Also
PEarc.dens.tri
and num.arcsPEtetra
Examples
A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0); D<-c(1/2,sqrt(3)/6,sqrt(6)/3)
tetra<-rbind(A,B,C,D)
n<-10 #try also n<-20
set.seed(1)
Xp<-runif.tetra(n,tetra)$g
M<-"CM" #try also M<-"CC"
r<-1.5
num.arcsPEtetra(Xp,tetra,r,M)
PEarc.dens.tetra(Xp,tetra,r,M)
PEarc.dens.tetra(Xp,tetra,r,M,th.cor = FALSE)