num.arcsPEtetra {pcds} | R Documentation |
An object of class "NumArcs"
.
Returns the number of arcs of
Proportional Edge Proximity Catch Digraphs (PE-PCDs)
whose vertices are the
given 3D numerical data set, Xp
.
It also provides number of vertices
(i.e., number of data points inside the tetrahedron)
and indices of the data points that reside in the tetrahedron.
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.
See also (Ceyhan (2005, 2010)).
num.arcsPEtetra(Xp, th, r, M = "CM")
Xp |
A set of 3D points which constitute the vertices of 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, |
A list
with the elements
desc |
A short description of the output: number of arcs and quantities related to the tetrahedron |
num.arcs |
Number of arcs of the PE-PCD |
tri.num.arcs |
Number of arcs of the induced subdigraph of the PE-PCD
for vertices in the tetrahedron |
num.in.tetra |
Number of |
ind.in.tetra |
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 tetrahedron |
vertices |
Vertices of the digraph, |
Elvan Ceyhan
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.
num.arcsPEtri
, num.arcsCStri
,
and num.arcsAStri
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<-1.25
Narcs = num.arcsPEtetra(Xp,tetra,r,M)
Narcs
summary(Narcs)
#plot(Narcs)