rassoc.multi.tri: Generation of points associated (in a Type I fashion) with a...

In pcds: Proximity Catch Digraphs and Their Applications

Generation of points associated (in a Type I fashion) with a given set of points

Description

An object of class "Patterns". Generates n points uniformly in the support for Type I association in the convex hull of set of points, Yp. delta is the parameter of association (that is, only \delta 100 % area around each vertex in each Delaunay triangle is allowed for point generation).

delta corresponds to eps in the standard equilateral triangle T_e as delta=4eps^2/3 (see rseg.std.tri function).

If Yp consists only of 3 points, then the function behaves like the function rassoc.tri.

DTmesh must be the Delaunay triangulation of Yp and DTr must be the corresponding Delaunay triangles (both DTmesh and DTr are NULL by default). If NULL, DTmesh is computed via tri.mesh and DTr is computed via triangles function in interp package.

tri.mesh function yields the triangulation nodes with their neighbours, and creates a triangulation object, and triangles function yields a triangulation data structure from the triangulation object created by tri.mesh (the first three columns are the vertex indices of the Delaunay triangles).

See (\insertCiteceyhan:arc-density-PE,ceyhan:arc-density-CS,ceyhan:dom-num-NPE-Spat2011;textualpcds) for more on the association pattern. Also, see (\insertCiteokabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

rassoc.multi.tri(n, Yp, delta, DTmesh = NULL, DTr = NULL)

Arguments

n	A positive integer representing the number of points to be generated.
Yp	A set of 2D points from which Delaunay triangulation is constructed.
delta	A positive real number in (0,1). delta is the parameter of association (that is, only \delta 100 % area around vertices of each Delaunay triangle is allowed for point generation).
DTmesh	Delaunay triangulation of Yp, default is NULL, which is computed via tri.mesh function in interp package. tri.mesh function yields the triangulation nodes with their neighbours, and creates a triangulation object.
DTr	Delaunay triangles based on Yp, default is NULL, which is computed via tri.mesh function in interp package. triangles function yields a triangulation data structure from the triangulation object created by tri.mesh.

Value

A list with the elements

type	The type of the pattern from which points are to be generated
mtitle	The "main" title for the plot of the point pattern
parameters	Attraction parameter, delta, of the Type I association pattern. delta is in (0,1) and only \delta 100 % of the area around vertices of each Delaunay triangle is allowed for point generation.
ref.points	The input set of points Yp; reference points, i.e., points with which generated points are associated.
gen.points	The output set of generated points associated with Yp points.
tri.Y	Logical output, TRUE if triangulation based on Yp points should be implemented.
desc.pat	Description of the point pattern
num.points	The vector of two numbers, which are the number of generated points and the number of reference (i.e., Yp) points.
xlimit, ylimit	The ranges of the x- and y-coordinates of the reference points, which are the Yp points

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

rassoc.circular, rassoc.std.tri, rassocII.std.tri, and rseg.multi.tri

Examples

#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-100; ny<-4;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
Yp<-cbind(runif(ny),runif(ny))
del<-.4

Xdt<-rassoc.multi.tri(nx,Yp,del)
Xdt
summary(Xdt)
plot(Xdt)

#or use
DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove")
#Delaunay triangulation based on Y points
TRY<-interp::triangles(DTY)[,1:3];
Xp<-rassoc.multi.tri(nx,Yp,del,DTY,TRY)$g
#data under CSR in the convex hull of Ypoints

Xlim<-range(Yp[,1])
Ylim<-range(Yp[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

#plot of the data in the convex hull of Y points together with the Delaunay triangulation
DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove")
#Delaunay triangulation based on Y points

plot(Xp,main="Points from Type I Association \n in Multipe Triangles",
xlab=" ", ylab=" ",xlim=Xlim+xd*c(-.05,.05),
ylim=Ylim+yd*c(-.05,.05),type="n")
interp::plot.triSht(DTY, add=TRUE,
do.points=TRUE,col="blue")
points(Xp,pch=".",cex=3)

pcds documentation built on May 29, 2024, 9:36 a.m.