pcds (version 0.1.8)

IarcCSset2pnt.tri: 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 ${\cup }_{xinS}{N}_{CS}(x,t)$, 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))

Value

I(p is in ${\cup }_{xinS}{N}_{CS}(x,t)$), 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

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.

Author

Elvan Ceyhan

See Also

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

Examples

# \donttest{
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)
# }