| plotASarcs {pcds} | R Documentation |
The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case
Description
Plots the arcs of AS-PCD whose vertices are the data points
in Xp and Delaunay triangles based on Yp points.
AS proximity regions are constructed with respect to the Delaunay triangles
based on Yp points, i.e.,
AS proximity regions are defined only for Xp points
inside the convex hull of Yp points.
That is, arcs may exist for Xp points only
inside the convex hull of Yp points.
If there are duplicates of Xp points,
only one point is retained for each duplicate value,
and a warning message is printed.
Vertex regions 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.
When the center is the circumcenter, CC,
the vertex regions are constructed based on the
orthogonal projections to the edges,
while with any interior center M,
the vertex regions are constructed using the extensions
of the lines combining vertices with M.
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, 2010)) for more on AS-PCDs. Also see (Okabe et al. (2000); Ceyhan (2010); Sinclair (2016)) for more on Delaunay triangulation and the corresponding algorithm.
Usage
plotASarcs(
Xp,
Yp,
M = "CC",
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 AS-PCD. |
Yp |
A set of 2D points which constitute the vertices of
the Delaunay triangulation. The Delaunay
triangles partition the convex hull of |
M |
The center of the triangle.
|
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 AS-PCD for a 2D data set Xp
where AS proximity regions
are defined with respect to the Delaunay triangles based on Yp points;
also plots 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 (2012).
“An investigation of new graph invariants related to the domination number of random proximity catch digraphs.”
Methodology and Computing in Applied Probability, 14(2), 299-334.
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
plotASarcs.tri, plotPEarcs.tri, plotPEarcs,
plotCSarcs.tri, and plotCSarcs
Examples
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-15; 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)
plotASarcs(Xp,Yp,M,asp=1,xlab="",ylab="")
plotASarcs(Xp,Yp[1:3,],M,asp=1,xlab="",ylab="")