pcds (version 0.1.8)

IarcPEtetra: The indicator for the presence of an arc from one 3D point to another 3D point for Proportional Edge Proximity Catch Digraphs (PE-PCDs)

Description

Returns \(I(\)p2 is in \(N_{PE}(p1,r))\) for 3D points p1 and p2, that is, returns 1 if p2 is in \(N_{PE}(p1,r)\), returns 0 otherwise, where \(N_{PE}(x,r)\) is the PE proximity region for point \(x\) with the expansion parameter \(r \ge 1\).

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". rv is the index of the vertex region p1 resides, with default=NULL.

If p1 and p2 are distinct and either of them are outside th, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

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

Usage

IarcPEtetra(p1, p2, th, r, M = "CM", rv = NULL)

Value

\(I(\)p2 is in \(N_{PE}(p1,r))\) for p1, that is, returns 1 if p2 is in \(N_{PE}(p1,r)\), returns 0 otherwise

Arguments

p1

A 3D point whose PE proximity region is constructed.

p2

A 3D point. The function determines whether p2 is inside the PE proximity region of p1 or not.

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".

rv

Index of the M-vertex region containing the point, either 1,2,3,4 (default is NULL).

Author

Elvan Ceyhan

References

See Also

IarcPEstd.tetra, IarcPEtri and IarcPEint

Examples

# \donttest{
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<-3  #try also n<-20

Xp<-runif.tetra(n,tetra)$g

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

IarcPEtetra(Xp[1,],Xp[2,],tetra,r)  #uses the default M="CM"
IarcPEtetra(Xp[1,],Xp[2,],tetra,r,M)

IarcPEtetra(c(.4,.4,.4),c(.5,.5,.5),tetra,r,M)

#or try
RV<-rel.vert.tetraCC(Xp[1,],tetra)$rv
IarcPEtetra(Xp[1,],Xp[3,],tetra,r,M,rv=RV)

P1<-c(.1,.1,.1)
P2<-c(.5,.5,.5)
IarcPEtetra(P1,P2,tetra,r,M)
# }