pcds (version 0.1.4)

IndNPEtri: 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 \(I(\)pt2 is in \(N_{PE}(pt1,r))\) for points pt1 and pt2, that is, returns 1 if pt2 is in \(N_{PE}(pt1,r)\), 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 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 pt1 resides, with default=NULL.

If pt1 and pt2 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

IndNPEtri(pt1, pt2, r, tri, M = c(1, 1, 1), rv = NULL)

Value

\(I(\)pt2 is in \(N_{PE}(pt1,r))\) for points pt1 and pt2, that is, returns 1 if pt2 is in \(N_{PE}(pt1,r)\), returns 0 otherwise

Arguments

pt1

A 2D point whose PE proximity region is constructed.

pt2

A 2D 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 \(\ge 1\).

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

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; 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

IndNPEbastri, IndNPETe, IndNAStri, and IndNCStri

Examples

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<-10
set.seed(1)
dat<-runif.tri(n,Tr)$g

IndNPEtri(dat[1,],dat[2,],r,Tr,M)

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

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

IndNPEtri(P2,P2,r,Tr,M)

P3<-c(1.7,.6)
IndNPEtri(P2,P3,r,Tr,M)
IndNPEtri(P3,P2,r,Tr,M)

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

P1<-c(1.4,1.2)
P2<-c(1.5,1.26)
IndNPEtri(P1,P2,r,Tr,M)
IndNPEtri(P2,P1,r,Tr,M)

#or try
Rv<-rv.tri.cent(P1,Tr,M)$rv
IndNPEtri(P1,P2,r,Tr,M,Rv)

P2<-c(1.8,.5)
P3<-c(1.7,.6)
IndNPEtri(P2,P3,r,Tr,M)

dat.fr<-data.frame(a=Tr)
IndNPEtri(P2,P3,r,dat.fr,M)