edgesCStri | R Documentation |
An object of class "UndPCDs"
.
Returns edges of the underlying or reflexivity graph of CS-PCD
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 constructed
with respect to the triangle tri
with expansion
parameter t > 0
, i.e.,
edges may exist only for points inside tri
.
It also provides various descriptions
and quantities about the edges of
the underlying or reflexivity graphs of the CS-PCD
such as number of edges, edge 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
.
With any interior center M
,
the edge regions are constructed using the extensions
of the lines combining vertices with M
.
See also (\insertCiteceyhan:Phd-thesis,ceyhan:stamet2016;textualpcds.ugraph).
edgesCStri(Xp, tri, 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 CS-PCD. |
tri |
A |
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 |
ugraph |
The type of the graph based on CS-PCDs,
|
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 the support triangle. |
tess.name |
Name of the tessellation points |
vertices |
Vertices of the underlying
or reflexivity graph of the digraph, |
vert.name |
Name of the data set which constitutes 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 CS-PCD 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
edgesCS
, edgesAStri
, edgesPEtri
,
and arcsCStri
#\donttest{
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10
set.seed(1)
Xp<-pcds::runif.tri(n,Tr)$g
M<-as.numeric(pcds::runif.tri(1,Tr)$g)
t<-1.5
#for underlying graph
Edges<-edgesCStri(Xp,Tr,t,M)
Edges
summary(Edges)
plot(Edges)
#for reflexivity graph
Edges<-edgesCStri(Xp,Tr,t,M,ugraph="r")
Edges
summary(Edges)
plot(Edges)
#can add edge regions
cent<-M
cent.name<-"M"
Ds<-pcds::prj.cent2edges(Tr,M)
L<-rbind(cent,cent,cent); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
#now we can add the vertex names and annotation
txt<-rbind(Tr,cent,Ds)
xc<-txt[,1]+c(-.02,.02,.02,.02,.03,-.03,-.01)
yc<-txt[,2]+c(.02,.02,.03,.06,.04,.05,-.07)
txt.str<-c("A","B","C","M","D1","D2","D3")
text(xc,yc,txt.str)
#}
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