num.arcsPEtetra: Number of arcs of Proportional Edge Proximity Catch Digraphs...

In pcds: Proximity Catch Digraphs and Their Applications

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the tetrahedron - one tetrahedron case

Description

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 (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010;textualpcds).

Usage

num.arcsPEtetra(Xp, th, r, M = "CM")

Arguments

Xp	A set of 3D points which constitute the vertices of PE-PCD.
th	A 4 \times 3 matrix with each row representing a vertex of the tetrahedron.
r	A positive real number which serves as the expansion parameter in PE proximity region; must be \ge 1.
M	The center to be used in the construction of the vertex regions in the tetrahedron, th. Currently it only takes "CC" for circumcenter and "CM" for center of mass; default="CM".

Value

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 th
num.in.tetra	Number of Xp points in the tetrahedron, th
ind.in.tetra	The vector of indices of the Xp points that reside in the tetrahedron
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 th.
vertices	Vertices of the digraph, Xp.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

num.arcsPEtri, num.arcsCStri, and num.arcsAStri

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<-1.25

Narcs = num.arcsPEtetra(Xp,tetra,r,M)
Narcs
summary(Narcs)
#plot(Narcs)

pcds documentation built on May 29, 2024, 9:36 a.m.