View source: R/ArcSliceFunctions.R
num.arcsAS | R Documentation |
An object of class "NumArcs"
.
Returns the number of arcs and various other quantities related to the Delaunay triangles
for Arc Slice Proximity Catch Digraph (AS-PCD) whose vertices are the data points in Xp
in the multiple triangle case.
AS proximity regions are defined with respect to the
Delaunay triangles based on Yp
points and vertex regions in each triangle
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.
Convex hull of Yp
is partitioned by the Delaunay triangles based on Yp
points
(i.e., multiple triangles are the set of these Delaunay triangles whose union constitutes
the convex hull of Yp
points).
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.
num.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 triangles. |
M |
The center of the triangle. |
A list
with the elements
desc |
A short description of the output: number of arcs and related quantities for the induced subdigraphs in the Delaunay triangles |
num.arcs |
Total number of arcs in all triangles, i.e., the number of arcs for the entire AS-PCD |
num.in.conhull |
Number of |
num.in.tris |
The vector of number of |
weight.vec |
The |
tri.num.arcs |
The |
del.tri.ind |
A matrix of indices of Delaunay triangles based on |
data.tri.ind |
A |
tess.points |
Points on which the tessellation of the study region is performed, here, tessellation
is the Delaunay triangulation based on |
vertices |
Vertices of the digraph, |
Elvan Ceyhan
num.arcsAStri
, num.arcsPE
, and num.arcsCS
## Not run:
nx<-15; ny<-5; #try also nx<-40; ny<-10 or nx<-1000; ny<-10;
set.seed(1)
Xp<-cbind(runif(nx),runif(nx))
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<-"CC" #try also M<-c(1,1,1)
Narcs = num.arcsAS(Xp,Yp,M)
Narcs
summary(Narcs)
plot(Narcs)
## End(Not run)
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