View source: R/ArcSliceFunctions.R
num.arcsAStri | R Documentation |
An object of class "NumArcs"
.
Returns the number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs)
whose vertices are the 2D data set, Xp
.
It also provides number of vertices (i.e., number of data points inside the triangle)
and indices of the data points that reside in the triangle.
The data points could be inside or outside a general
triangle tri
=T(A,B,C)=
(rv=1,rv=2,rv=3)
, with vertices of tri
stacked row-wise.
AS proximity regions are defined with respect to the triangle tri
and vertex regions are
based on the center M="CC"
for circumcenter of tri
;
or 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="CC"
i.e., circumcenter of tri
.
For the number of arcs, loops are not allowed,
so arcs are only possible for points inside the triangle, tri
.
See also (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).
num.arcsAStri(Xp, tri, M = "CC")
Xp |
A set of 2D points which constitute the vertices of the digraph (i.e., AS-PCD). |
tri |
Three 2D points, stacked row-wise, each row representing a vertex of the triangle. |
M |
The center of the triangle. |
A list
with the elements
desc |
A short description of the output: number of arcs and quantities related to the triangle |
num.arcs |
Number of arcs of the AS-PCD |
num.in.tri |
Number of |
ind.in.tri |
The vector of indices of the |
tess.points |
Points on which the tessellation of the study region is performed, here, tessellation is the support triangle. |
vertices |
Vertices of the digraph, |
Elvan Ceyhan
num.arcsAS
, num.arcsPEtri
, and num.arcsCStri
## Not run:
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10 #try also n<-20
set.seed(1)
Xp<-runif.tri(n,Tr)$g
M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.2)
Narcs = num.arcsAStri(Xp,Tr,M)
Narcs
summary(Narcs)
plot(Narcs)
## End(Not run)
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