IedgeCStri  R Documentation 
Returns I(
p1p2
is an edge
in the underlying or reflexivity graph of CSPCDs )
for points p1
and p2
in a given triangle.
More specifically, when the argument ugraph="underlying"
, it returns
the edge indicator for the CSPCD underlying graph,
that is, returns 1 if p2
is
in N_{CS}(p1,t)
or p1
is in N_{CS}(p2,t)
,
returns 0 otherwise.
On the other hand,
when ugraph="reflexivity"
, it returns
the edge indicator for the CSPCD reflexivity graph,
that is, returns 1 if p2
is
in N_{CS}(p1,t)
and p1
is in N_{CS}(p2,t)
,
returns 0 otherwise.
In both cases CS proximity region is constructed
with respect to the triangle tri
and
edge regions are based on the center, M=(m_1,m_2)
in Cartesian coordinates or
M=(\alpha,\beta,\gamma)
in barycentric coordinates
in the interior of tri
;
default is M=(1,1,1)
, i.e.,
the center of mass of tri
.
If p1
and p2
are distinct
and either of them are outside tri
, it returns 0,
but if they are identical,
then it returns 1 regardless of their locations
(i.e., it allows loops).
See also (\insertCiteceyhan:Phdthesis,ceyhan:stamet2016;textualpcds.ugraph).
IedgeCStri(
p1,
p2,
tri,
t,
M = c(1, 1, 1),
ugraph = c("underlying", "reflexivity")
)
p1 
A 2D point whose CS proximity region is constructed. 
p2 
A 2D point. The function determines
whether there is an edge from 
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 CSPCDs,

Returns 1 if there is an edge between points p1
and p2
in the underlying or reflexivity graph of CSPCDs
in a given triangle tri
, and 0 otherwise.
Elvan Ceyhan
IedgeCSbasic.tri
, IedgeAStri
,
IedgePEtri
and IarcCStri
#\donttest{
A<c(1,1); B<c(2,0); C<c(1.5,2);
Tr<rbind(A,B,C);
M<as.numeric(pcds::runif.tri(1,Tr)$g)
t<1.5
n<3
set.seed(1)
Xp<pcds::runif.tri(n,Tr)$g
IedgeCStri(Xp[1,],Xp[2,],Tr,t,M)
IedgeCStri(Xp[1,],Xp[2,],Tr,t,M,ugraph = "reflexivity")
P1<as.numeric(pcds::runif.tri(1,Tr)$g)
P2<as.numeric(pcds::runif.tri(1,Tr)$g)
IedgeCStri(P1,P2,Tr,t,M)
IedgeCStri(P1,P2,Tr,t,M,ugraph="r")
#}
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