| plotPEarcs {pcds} | R Documentation |
The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case
Description
Plots the arcs of Proportional Edge Proximity Catch Digraph
(PE-PCD) whose vertices are the data
points in Xp in the multiple triangle case
and the Delaunay triangles based on Yp points.
If there are duplicates of Xp points,
only one point is retained for each duplicate value,
and a warning message is printed.
PE proximity regions are defined
with respect to the Delaunay triangles based on Yp points
with expansion parameter r \ge 1
and vertex regions in each triangle are
based on the center M=(\alpha,\beta,\gamma)
in barycentric coordinates in the interior of each Delaunay triangle
or based on circumcenter of
each Delaunay triangle (default for M=(1,1,1)
which is the center of mass of the 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).
Loops are not allowed so arcs are only possible
for points inside the convex hull of Yp points.
See (Ceyhan (2005); Ceyhan et al. (2006); Ceyhan (2011)) for more on the PE-PCDs. Also, see (Okabe et al. (2000); Ceyhan (2010); Sinclair (2016)) for more on Delaunay triangulation and the corresponding algorithm.
Usage
plotPEarcs(
Xp,
Yp,
r,
M = c(1, 1, 1),
asp = NA,
main = NULL,
xlab = NULL,
ylab = NULL,
xlim = NULL,
ylim = NULL,
...
)
Arguments
Xp |
A set of 2D points which constitute the vertices of the PE-PCD. |
Yp |
A set of 2D points which constitute the vertices of the Delaunay triangles. |
r |
A positive real number
which serves as the expansion parameter in PE proximity region;
must be |
M |
A 3D point in barycentric coordinates
which serves as a center in the interior of each Delaunay
triangle or circumcenter of each Delaunay triangle
(for this, argument should be set as |
asp |
A |
main |
An overall title for the plot (default= |
xlab, ylab |
Titles for the |
xlim, ylim |
Two |
... |
Additional |
Value
A plot of the arcs of the PE-PCD
whose vertices are the points in data set Xp and the Delaunay
triangles based on Yp points
Author(s)
Elvan Ceyhan
References
Ceyhan E (2005).
An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications.
Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.
Ceyhan E (2010).
“Extension of One-Dimensional Proximity Regions to Higher Dimensions.”
Computational Geometry: Theory and Applications, 43(9), 721-748.
Ceyhan E (2011).
“Spatial Clustering Tests Based on Domination Number of a New Random Digraph Family.”
Communications in Statistics - Theory and Methods, 40(8), 1363-1395.
Ceyhan E, Priebe CE, Wierman JC (2006).
“Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.”
Computational Statistics & Data Analysis, 50(8), 1925-1964.
Okabe A, Boots B, Sugihara K, Chiu SN (2000).
Spatial Tessellations: Concepts and Applications of Voronoi Diagrams.
Wiley, New York.
Sinclair D (2016).
“S-hull: a fast radial sweep-hull routine for Delaunay triangulation.”
1604.01428.
See Also
plotPEarcs.tri, plotASarcs,
and plotCSarcs
Examples
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-5; #try also nx<-40; ny<-10 or nx<-1000; ny<-10;
set.seed(1)
Xp<-cbind(runif(nx,0,1),runif(nx,0,1))
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<-c(1,1,1) #try also M<-c(1,2,3)
r<-1.5 #try also r<-2
plotPEarcs(Xp,Yp,r,M,xlab="",ylab="")