| plotASedges {pcds.ugraph} | R Documentation |
The plot of the edges of the underlying or reflexivity graph of the Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - multiple triangle case
Description
Plots the edges of the underlying or reflexivity graph of
the Arc Slice Proximity Catch Digraph
(AS-PCD) whose vertices are the data
points in Xp in the multiple triangle case
and the 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, edges may exist for Xp points
only inside the convex hull of Yp points.
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 edges are only possible
for points inside the convex hull of Yp points.
See (Ceyhan (2005, 2016)) for more on the AS-PCDs. Also, see (Okabe et al. (2000); Ceyhan (2010); Sinclair (2016)) for more on Delaunay triangulation and the corresponding algorithm.
Usage
plotASedges(
Xp,
Yp,
M = "CC",
ugraph = c("underlying", "reflexivity"),
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 underlying or reflexivity graphs of the AS-PCD. |
Yp |
A set of 2D points which constitute the vertices of the Delaunay triangles. |
M |
The center of the triangle.
|
ugraph |
The type of the graph based on AS-PCDs,
|
asp |
A |
main |
An overall title for the plot (default= |
xlab, ylab |
Titles for the |
xlim, ylim |
Two |
... |
Additional |
Value
A plot of the edges of the underlying
or reflexivity graphs 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 (2016).
“Edge Density of New Graph Types Based on a Random Digraph Family.”
Statistical Methodology, 33, 31-54.
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
plotASedges.tri, plotPEedges,
plotCSedges, and plotASarcs
Examples
#\donttest{
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-5;
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))
M<-c(1,1,1)
plotASedges(Xp,Yp,M,xlab="",ylab="")
plotASedges(Xp,Yp,M,xlab="",ylab="",ugraph="r")
#}