edgesCS  R Documentation 
An object of class "UndPCDs"
.
Returns edges of the underlying or reflexivity graph of CSPCD
as left and right end points
and related parameters and the quantities of these graphs.
The vertices of these graphs are the data points in Xp
in the multiple triangle case.
CS proximity regions are
defined with respect to the Delaunay triangles
based on Yp
points with expansion parameter t > 0
and
edge regions in each triangle are
based on the center M=(\alpha,\beta,\gamma)
in barycentric coordinates
in the interior of each Delaunay triangle
(default for M=(1,1,1)
which is the center of mass of the triangle).
Each Delaunay triangle is first converted to
an (nonscaled) basic triangle so that M
will be the same
type of center for each Delaunay triangle
(this conversion is not necessary when M
is CM
).
Convex hull of Yp
is partitioned
by the Delaunay triangles based on Yp
points
(i.e., multiple triangles are the set of these Delaunay triangles
whose union constitutes the
convex hull of Yp
points).
For the number of edges, loops are not allowed so edges are only possible
for points inside the convex hull of Yp
points.
See (\insertCiteceyhan:Phdthesis,ceyhan:stamet2016;textualpcds.ugraph) for more on the CSPCDs. Also, see (\insertCiteokabe:2000,ceyhan:compgeo2010,sinclair:2016;textualpcds.ugraph) for more on Delaunay triangulation and the corresponding algorithm.
edgesCS(Xp, Yp, t, M = c(1, 1, 1), ugraph = c("underlying", "reflexivity"))
Xp 
A set of 2D points which constitute the vertices of the underlying or reflexivity graphs of the CSPCD. 
Yp 
A set of 2D points which constitute the vertices of the Delaunay triangles. 
t 
A positive real number which serves as the expansion parameter in CS proximity region. 
M 
A 3D point in barycentric coordinates
which serves as a center in the interior of each Delaunay triangle,
default for 
ugraph 
The type of the graph based on CSPCDs,

A list
with the elements
type 
A description of the underlying or reflexivity graph of the digraph 
parameters 
Parameters of
the underlying or reflexivity graph of the digraph,
the center 
tess.points 
Tessellation points, i.e.,
points on which the tessellation
of the study region is performed, here, tessellation
is Delaunay triangulation based on 
tess.name 
Name of the tessellation points 
vertices 
Vertices of the underlying and
reflexivity graph of the digraph, 
vert.name 
Name of the data set which constitute the vertices of the underlying or reflexivity graph of the digraph 
LE , RE 
Left and right end points of the edges of
the underlying or reflexivity graph of CSPCD for 2D data set 
mtitle 
Text for 
quant 
Various quantities for the underlying or reflexivity graph of the digraph: number of vertices, number of partition points, number of intervals, number of edges, and edge density. 
Elvan Ceyhan
edgesCStri
, edgesAS
, edgesPE
,
and arcsCS
#\donttest{
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<20; ny<5;
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))
M<c(1,1,1)
t<1.5
Edges<edgesCS(Xp,Yp,t,M)
Edges
summary(Edges)
plot(Edges)
Edges<edgesCS(Xp,Yp,t,M,ugraph="r")
Edges
summary(Edges)
plot(Edges)
#}
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