NumArcsCStri: Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

Description

Returns the number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) whose vertices are the given 2D numerical data set, dat.

CS proximity region $N_{C S} (x, t)$ is defined with respect to the triangle, tri with expansion parameter $t > 0$ and edge regions are based on the center $M = (m_{1}, m_{2})$ in Cartesian coordinates or $M = (α, β, γ)$ in barycentric coordinates in the interior of tri; default is $M = (1, 1, 1)$ i.e., the center of mass of tri. For the number of arcs, loops are not allowed so arcs are only possible for points inside tri for this function.

See also (ceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

NumArcsCStri(Dt, tri, t, M = c(1, 1, 1))

Arguments

A set of 2D points which constitute the vertices of CS-PCD.

tri

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

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

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

Number of arcs for the CS-PCD with vertices being 2D data set, dat, in tri with expansion parameter, $t > 0$ , and center of mass CM. CS proximity regions are defined only for Dt points inside tri, i.e., arcs are possible for such points only.

References

Examples

Run this code

# NOT RUN {
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);

n<-10  #try also n<-20
set.seed(1)
dat<-runif.tri(n,Tr)$g

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

NumArcsCStri(dat,Tr,t=.5,M)
NumArcsCStri(dat,Tr,t=1,M)
NumArcsCStri(dat,Tr,t=1.5,M)

NumArcsCStri(c(1.4,.2),Tr,t=.5,M)

t<-.5
NumArcsCStri(dat,Tr,t,M)

dat.fr<-data.frame(a=dat)
NumArcsCStri(dat.fr,Tr,t,M)

dat.fr<-data.frame(a=Tr)
NumArcsCStri(dat,dat.fr,t,M)

# }

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