pcds (version 0.1.8)

IarcPEtri: The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

Description

Returns \(I(\)p2 is in \(N_{PE}(p1,r))\) for points p1 and p2, that is, returns 1 if p2 is in \(N_{PE}(p1,r)\), and 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 triangle tri and vertex regions are based on the center, \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of tri or based on the circumcenter of tri; default is \(M=(1,1,1)\), i.e., the center of mass of tri. 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 tri, 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:arc-density-PE,ceyhan:dom-num-NPE-Spat2011;textualpcds).

Usage

IarcPEtri(p1, p2, tri, r, M = c(1, 1, 1), rv = NULL)

Value

\(I(\)p2 is in \(N_{PE}(p1,r))\)

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

Arguments

p1

A 2D point whose PE proximity region is constructed.

p2

A 2D point. The function determines whether p2 is inside the PE proximity region of p1 or not.

tri

A \(3 \times 2\) matrix with each row representing a vertex of the triangle.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri or the circumcenter of tri which may be entered as "CC" as well; default is \(M=(1,1,1)\), i.e., the center of mass of tri.

rv

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

Author

Elvan Ceyhan

References

See Also

IarcPEbasic.tri, IarcPEstd.tri, IarcAStri, and IarcCStri

Examples

# \donttest{
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0);

r<-1.5

n<-3
set.seed(1)
Xp<-runif.tri(n,Tr)$g

IarcPEtri(Xp[1,],Xp[2,],Tr,r,M)

P1<-as.numeric(runif.tri(1,Tr)$g)
P2<-as.numeric(runif.tri(1,Tr)$g)
IarcPEtri(P1,P2,Tr,r,M)

P1<-c(.4,.2)
P2<-c(1.8,.5)
IarcPEtri(P1,P2,Tr,r,M)
IarcPEtri(P2,P1,Tr,r,M)

M<-c(1.3,1.3)
r<-2

#or try
Rv<-rel.vert.tri(P1,Tr,M)$rv
IarcPEtri(P1,P2,Tr,r,M,Rv)
# }