IarcCSset2pnt.tri {pcds}

The indicator for the presence of an arc from a point in set S to the point p for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

Description

Returns I(p in N_{CS}(x,t) for some x in S), that is, returns 1 if p in \cup_{x in S} N_{CS}(x,t), returns 0 otherwise.

CS proximity region is constructed with respect to the triangle tri with the expansion parameter t>0 and edge 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 the triangle tri; default is M=(1,1,1) i.e., the center of mass of tri.

Edges of tri=T(A,B,C), AB, BC, AC, are also labeled as edges 3, 1, and 2, respectively. If p is not in S and either p or all points in S are outside tri, it returns 0, but if p is in S, then it always returns 1 regardless of its location (i.e., loops are allowed).

Usage

IarcCSset2pnt.tri(S, p, tri, t, M = c(1, 1, 1))

Arguments

S

A set of 2D points. Presence of an arc from a point in S to point p is checked by the function.

p

A 2D point. Presence of an arc from a point in S to point p is checked by the function.

tri

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

t

A positive real number which serves as the expansion parameter in CS proximity region constructed in the triangle tri.

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; default is M=(1,1,1) i.e., the center of mass of tri.

Value

I(p is in \cup_{x in S} N_{CS}(x,t)), that is, returns 1 if p is in S or inside N_{CS}(x,t) for at least one x in S, returns 0 otherwise where CS proximity region is constructed with respect to the triangle tri

Author(s)

Elvan Ceyhan

See Also

IarcCSset2pnt.std.tri, IarcCStri, IarcCSstd.tri, IarcASset2pnt.tri, and IarcPEset2pnt.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

set.seed(1)
Xp<-runif.tri(n,Tr)$gen.points

S<-rbind(Xp[1,],Xp[2,])  #try also S<-c(1.5,1)

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

tau<-.5

IarcCSset2pnt.tri(S,Xp[3,],Tr,tau,M)
IarcCSset2pnt.tri(S,Xp[3,],Tr,t=1,M)
IarcCSset2pnt.tri(S,Xp[3,],Tr,t=1.5,M)

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
IarcCSset2pnt.tri(S,Xp[3,],Tr,tau,M)