ArcsCStri: The arcs of Central Similarity Proximity Catch Digraphs...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

The arcs of Central Similarity Proximity Catch Digraphs (CS-PCD) for 2D data - one triangle case

Description

An object of class "PCDs". Returns arcs as tails (or sources) and heads (or arrow ends) for data set Xp as the vertices of CS-PCD and related parameters and the quantities of the digraph.

CS proximity regions are constructed with respect to the triangle tri with expansion parameter t>0, i.e., arcs may exist for points only inside tri. It also provides various descriptions and quantities about the arcs of the CS-PCD such as number of arcs, arc density, etc.

Edge regions are based on 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.

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

Usage

arcsCStri(Xp, tri, t, M = c(1, 1, 1))

Arguments

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

Value

A list with the elements

type	A description of the type of the digraph
parameters	Parameters of the digraph, the center M used to construct the edge regions and the expansion parameter t.
tess.points	Points on which the tessellation of the study region is performed, here, tessellation is the support triangle.
tess.name	Name of data set used in tessellation (i.e., vertices of the triangle)
vertices	Vertices of the digraph, Xp points
vert.name	Name of the data set which constitute the vertices of the digraph
S	Tails (or sources) of the arcs of CS-PCD for 2D data set Xp as vertices of the digraph
E	Heads (or arrow ends) of the arcs of CS-PCD for 2D data set Xp as vertices of the digraph
mtitle	Text for "main" title in the plot of the digraph
quant	Various quantities for the digraph: number of vertices, number of partition points, number of triangles, number of arcs, and arc density.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

arcsCS, arcsAStri and arcsPEtri

Examples

## Not run: 
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)$g

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

t<-1.5  #try also t<-2

Arcs<-arcsCStri(Xp,Tr,t,M)
#or try with the default center Arcs<-arcsCStri(Xp,Tr,t); M= (Arcs$param)$c
Arcs
summary(Arcs)
plot(Arcs)

#can add edge regions
L<-rbind(M,M,M); R<-Tr
segments(L[,1], L[,2], R[,1], R[,2], lty=2)

#now we can add the vertex names and annotation
txt<-rbind(Tr,M)
xc<-txt[,1]+c(-.02,.03,.02,.03)
yc<-txt[,2]+c(.02,.02,.03,.06)
txt.str<-c("A","B","C","M")
text(xc,yc,txt.str)

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.