plotASregs {pcds}

The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - multiple triangle case

Description

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.

Usage

plotASregs(
  Xp,
  Yp,
  M = "CC",
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

Arguments

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 Yp points.

M

The center of the triangle. "CC" stands for circumcenter of each Delaunay triangle or 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle; default is M="CC" i.e., the circumcenter of each triangle.

main

An overall title for the plot (default=NULL).

xlab, ylab

Titles for the x and y axes, respectively (default=NULL for both).

xlim, ylim

Two numeric vectors of length 2, giving the x- and y-coordinate ranges (default=NULL for both).

...

Additional plot parameters.

Value

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

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

plotASregs.tri, plotPEregs.tri, plotPEregs, plotCSregs.tri, and plotCSregs

Examples

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="")