pcds (version 0.1.4)

funsIndDelTri: Functions provide the indices of the Delaunay triangles where the points reside

Description

Two functions: ind.Del.tri and indices.Del.tri.

ind.Del.tri finds the index of the Delaunay triangle in which the given point, pt, resides.

indices.Del.tri finds the indices of triangles for all the points in data set, dat, as a vector.

Delaunay triangulation is based on Yp and DTmesh are the Delaunay triangles with default NULL. The function returns NA for a point not inside the convex hull of Yp. Number of Yp points (i.e., size of Yp) should be at least three and the points should be in general position so that Delaunay triangulation is (uniquely) defined.

If the number of Yp points is 3, then there is only one Delaunay triangle and the indices of all the points inside this triangle are all 1.

See (okabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

ind.Del.tri(pt, Yp, DTmesh = NULL)
indices.Del.tri(dat, Yp, DTmesh = NULL)

Value

ind.Del.tri returns the index of the Delaunay triangle in which the given point, pt, resides and indices.Del.tri returns the vector of indices of the Delaunay triangles in which points in the data set, dat, reside.

Arguments

pt

A 2D point; the index of the Delaunay triangle in which pt resides is to be determined. It is an argument for ind.Del.tri.

Yp

A set of 2D points from which Delaunay triangulation is constructed.

DTmesh

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.

dat

A set of 2D points representing the set of data points for which the indices of the Delaunay triangles they reside is to be determined. It is an argument for indices.Del.tri.

Author

Elvan Ceyhan

References

Examples

#Examples for ind.Del.tri
nx<-100 #number of X points (target)
ny<-10 #number of Y points (nontarget)

Yp<-cbind(runif(ny),runif(ny))

dat<-runifMT(nx,Yp)$g #data under CSR in the convex hull of Ypoints
#try also dat<-cbind(runif(nx),runif(nx))

ind.Del.tri(dat[10,],Yp)

#or use
DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove")  #Delaunay triangulation
TRY<-interp::triangles(DTY)[,1:3];
ind.Del.tri(dat[10,],Yp,DTY)

ind.Del.tri(c(.5,.5),Yp)

ind.Del.tri(c(1.5,.5),Yp)

ind.DT<-vector()
for (i in 1:nx)
 ind.DT<-c(ind.DT,ind.Del.tri(dat[i,],Yp))
ind.DT

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

DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove")  #Delaunay triangulation based on Y points

#plot of the data in the convex hull of Y points together with the Delaunay triangulation
plot(dat,main=" ", 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,pch=16,col="blue")
points(dat,pch=".",cex=3)
text(dat,labels = factor(ind.DT) )

Yp<-rbind(c(.3,.2),c(.4,.5),c(.14,.15))
ind.Del.tri(c(.25,.25),Yp)

dat.fr<-data.frame(a=Yp)
ind.Del.tri(c(.25,.25),dat.fr)

#Examples for indices.Del.tri
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-4;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
Yp<-cbind(runif(ny),runif(ny))
dat<-runifMT(nx,Yp)$g #data under CSR in the convex hull of Ypoints
#try also dat<-cbind(runif(nx),runif(nx))

tr.ind<-indices.Del.tri(dat,Yp)  #indices of the Delaunay triangles
tr.ind

#or use
DTY<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove")  #Delaunay triangulation based on Y points
tr.ind<-indices.Del.tri(dat,Yp,DTY)  #indices of the Delaunay triangles
tr.ind

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

oldpar <- par(no.readonly = TRUE)
par(pty="s")
plot(dat,main=" ", xlab=" ", ylab=" ",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05),pch=".")
interp::plot.triSht(DTY, add=TRUE, do.points = TRUE,pch=16,col="blue")
text(dat,labels = factor(tr.ind) )
par(oldpar)

Yp<-rbind(c(.3,.2),c(.4,.5),c(.14,.15))
indices.Del.tri(c(.25,.25),Yp)

dat<-rbind(c(.25,.25),c(.15,.25))
indices.Del.tri(dat,Yp)

dat.fr<-data.frame(a=dat)
indices.Del.tri(dat.fr,Yp)

dat.fr<-data.frame(a=Yp)
indices.Del.tri(c(.25,.25),dat.fr)