arcsAS: The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a...

In pcds: Proximity Catch Digraphs and Their Applications

The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case

Description

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

AS proximity regions are defined with respect to the Delaunay triangles based on Yp points, i.e., AS proximity regions are defined only for Xp points inside the convex hull of Yp points. That is, arcs may exist for points only inside the convex hull of Yp points. It also provides various descriptions and quantities about the arcs of the AS-PCD such as number of arcs, arc density, etc.

Vertex regions are based on the center M="CC" for circumcenter of each Delaunay triangle or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of each Delaunay triangle; default is M="CC" i.e., circumcenter of each triangle. M must be entered in barycentric coordinates unless it is the circumcenter.

See (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds) for more on AS PCDs. Also see (\insertCiteokabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

arcsAS(Xp, Yp, M = "CC")

Arguments

Xp	A set of 2D points which constitute the vertices of the AS-PCD.
Yp	A set of 2D points which constitute the vertices of the Delaunay triangulation. The Delaunay triangles partition the convex hull of Yp points.
M	The center of the triangle. "CC" represents the circumcenter of each Delaunay triangle or 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle; default is M="CC" i.e., the circumcenter of each triangle. M must be entered in barycentric coordinates unless it is the circumcenter.

Value

A list with the elements

type	A description of the type of the digraph
parameters	Parameters of the digraph, here, it is the center used to construct the vertex regions, default is circumcenter, denoted as "CC", otherwise given in barycentric coordinates.
tess.points	Points on which the tessellation of the study region is performed, here, tessellation is the Delaunay triangulation based on Yp points.
tess.name	Name of data set used in tessellation, i.e., Yp
vertices	Vertices of the digraph, Xp.
vert.name	Name of the data set which constitute the vertices of the digraph
S	Tails (or sources) of the arcs of AS-PCD for 2D data set Xp in the multiple triangle case as the vertices of the digraph
E	Heads (or arrow ends) of the arcs of AS-PCD for 2D data set Xp in the multiple triangle case as the 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 intervals, number of arcs, and arc density.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

arcsAStri, arcsPEtri, arcsCStri, arcsPE, and arcsCS

Examples

## Not run: 
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-15; ny<-5;  #try also nx=20; nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
Xp<-cbind(runif(nx,0,1),runif(nx,0,1))
Yp<-cbind(runif(ny,0,.25),runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))

M<-c(1,1,1)  #try also M<-c(1,2,3)

Arcs<-arcsAS(Xp,Yp,M) #try also the default M with Arcs<-arcsAS(Xp,Yp)
Arcs
summary(Arcs)
plot(Arcs)

arcsAS(Xp,Yp[1:3,],M)

## End(Not run)

pcds documentation built on July 9, 2023, 5:54 p.m.