arcsAS | R Documentation |
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.
arcsAS(Xp, Yp, M = "CC")
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 |
M |
The center of the triangle. |
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 |
tess.points |
Points on which the tessellation of the study region is performed, here, tessellation
is the Delaunay triangulation based on |
tess.name |
Name of data set used in tessellation, i.e., |
vertices |
Vertices of the digraph, |
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 |
E |
Heads (or arrow ends) of the arcs of AS-PCD for 2D data set |
mtitle |
Text for |
quant |
Various quantities for the digraph: number of vertices, number of partition points, number of intervals, number of arcs, and arc density. |
Elvan Ceyhan
arcsAStri
, arcsPEtri
, arcsCStri
, arcsPE
,
and arcsCS
## 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)
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