NPEbasic.tri | R Documentation |
Returns the vertices of the PE proximity region
(which is itself a triangle) for a point in the
standard basic triangle
T_b=T((0,0),(1,0),(c_1,c_2))=
(rv=1,rv=2,rv=3)
.
PE proximity region is defined with respect
to the standard basic triangle T_b
with expansion parameter r \ge 1
and vertex regions based on center M=(m_1,m_2)
in
Cartesian coordinates or M=(\alpha,\beta,\gamma)
in barycentric coordinates in the interior of the basic
triangle T_b
or based on the circumcenter of T_b
;
default is M=(1,1,1)
, i.e., the center of mass of T_b
.
Vertex regions are labeled as 1,2,3
rowwise for the vertices
of the triangle T_b
. rv
is the index of the vertex region
p
resides, with default=NULL
.
If p
is outside of tri
,
it returns NULL
for the proximity region.
See also (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).
NPEbasic.tri(p, r, c1, c2, M = c(1, 1, 1), rv = NULL)
p |
A 2D point whose PE proximity region is to be computed. |
r |
A positive real number which serves
as the expansion parameter in PE proximity region;
must be |
c1, c2 |
Positive real numbers
representing the top vertex in standard basic triangle
|
M |
A 2D point in Cartesian coordinates or a 3D point
in barycentric coordinates
which serves as a center
in the interior of the standard basic triangle |
rv |
Index of the |
Vertices of the triangular region
which constitutes the PE proximity region with expansion parameter
r and center M
for a point p
Elvan Ceyhan
NPEtri
, NAStri
, NCStri
,
and IarcPEbasic.tri
## Not run:
c1<-.4; c2<-.6
A<-c(0,0); B<-c(1,0); C<-c(c1,c2);
Tb<-rbind(A,B,C);
M<-as.numeric(runif.basic.tri(1,c1,c2)$g) #try also M<-c(.6,.2)
r<-2
P1<-as.numeric(runif.basic.tri(1,c1,c2)$g) #try also P1<-c(.4,.2)
NPEbasic.tri(P1,r,c1,c2,M)
#or try
Rv<-rel.vert.basic.tri(P1,c1,c2,M)$rv
NPEbasic.tri(P1,r,c1,c2,M,Rv)
P1<-c(1.4,1.2)
P2<-c(1.5,1.26)
NPEbasic.tri(P1,r,c1,c2,M) #gives an error if M=c(1.3,1.3)
#since center is not the circumcenter or not in the interior of the triangle
## End(Not run)
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