IndNPEtetra: 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 $I ($ pt2 is in $N_{P E} (p t 1, r))$ for 3D points pt1 and pt2, that is, returns 1 if pt2 is in $N_{P E} (p t 1, r)$ , returns 0 otherwise, where N_PE(x,r) is the PE proximity region for point $x$ with the expansion parameter $r \geq 1$ .

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 pt1 resides, with default=NULL.

If pt1 and pt2 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

IndNPEtetra(pt1, pt2, r, th, M = "CM", rv = NULL)

Value

$I ($ pt2 is in $N_{P E} (p t 1, r))$ for pt1, that is, returns 1 if pt2 is in $N_{P E} (p t 1, r)$ , returns 0 otherwise

Arguments

pt1: A 3D point whose PE proximity region is constructed.
pt2: A 3D point. The function determines whether pt2 is inside the PE proximity region of pt1 or not.
r: A positive real number which serves as the expansion parameter in PE proximity region; must be $\geq 1$ .
th: Four 3D points, stacked row-wise, each row representing a vertex of the tetrahedron.
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

Examples

Run this code

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

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

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

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

IndNPEtetra(dat[1,],dat[1,],r,tetra,M)

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

#or try
RV<-rv.tetraCC(dat[1,],tetra)$rv
IndNPEtetra(dat[1,],dat[5,],r,tetra,M,rv=RV)

IndNPEtetra(dat[1,],c(-1,-1,-1),r,tetra,M,rv=NULL)

IndNPEtetra(c(-1,-1,-1),dat[1,],r,tetra,M,rv=NULL)
IndNPEtetra(c(-1,-1,-1),c(-1,-1,-1),r,tetra,M)

P1<-c(.1,.1,.1)
P2<-c(.5,.5,.5)
IndNPEtetra(P1,P2,r,tetra,M)

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