inci.matPEtetra: Incidence matrix for Proportional Edge Proximity Catch...

In pcds: Proximity Catch Digraphs and Their Applications

Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case

Description

Returns the incidence matrix for the PE-PCD whose vertices are the given 3D numerical data set, Xp, in the tetrahedron th=T(v=1,v=2,v=3,v=4).

PE proximity regions are constructed with respect to tetrahedron th with expansion parameter r \ge 1 and vertex regions are based on the center M which is circumcenter ("CC") or center of mass ("CM") of th with default="CM". Loops are allowed, so the diagonal entries are all equal to 1.

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

Usage

inci.matPEtetra(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

Incidence matrix for the PE-PCD with vertices being 3D data set, Xp, in the tetrahedron th with vertex regions based on circumcenter or center of mass

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

inci.matPEtri, inci.matPE1D, and inci.matPE

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<-5

Xp<-runif.tetra(n,tetra)$g  #try also Xp<-c(.5,.5,.5)

M<-"CM"  #try also M<-"CC"
r<-1.5

IM<-inci.matPEtetra(Xp,tetra,r=1.25)  #uses the default M="CM"
IM<-inci.matPEtetra(Xp,tetra,r=1.25,M)
IM
dom.num.greedy(IM)
Idom.num.up.bnd(IM,3) #try also dom.num.exact(IM)  #this might take a long time for large n

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