plotASregs {pcds} | R Documentation |
Plots the Xp
points in and outside of the convex hull of Yp
points and also plots the AS proximity regions
for Xp
points and Delaunay triangles based on Yp
points.
AS proximity regions are constructed with respect
to the Delaunay triangles based on Yp
points (these triangles partition the convex hull of Yp
points),
i.e., AS proximity regions are only defined for Xp
points 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.
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.
plotASregs(
Xp,
Yp,
M = "CC",
main = NULL,
xlab = NULL,
ylab = NULL,
xlim = NULL,
ylim = NULL,
...
)
Xp |
A set of 2D points for which AS proximity regions are constructed. |
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. |
main |
An overall title for the plot (default= |
xlab , ylab |
Titles for the |
xlim , ylim |
Two |
... |
Additional |
Plot of the Xp
points, Delaunay triangles based on Yp
and also the AS proximity regions
for Xp
points inside the convex hull of Yp
points
Elvan Ceyhan
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.
plotASregs.tri
, plotPEregs.tri
, plotPEregs
,
plotCSregs.tri
, and plotCSregs
nx<-10 ; 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))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))
M<-c(1,1,1) #try also M<-c(1,2,3) #or M="CC"
plotASregs(Xp,Yp,M,xlab="",ylab="")
plotASregs(Xp,Yp[1:3,],M,xlab="",ylab="")
Xp<-c(.5,.5)
plotASregs(Xp,Yp,M,xlab="",ylab="")