fr2vertsCCvert.reg: The furthest points in a data set from vertices in each...

In pcds: Proximity Catch Digraphs and Their Applications

The furthest points in a data set from vertices in each CC-vertex region in a triangle

Description

An object of class "Extrema". Returns the furthest data points among the data set, Xp, in each CC-vertex region from the vertex in the triangle, tri=T(A,B,C). Vertex region labels/numbers correspond to the row number of the vertex in tri. ch.all.intri is for checking whether all data points are inside tri (default is FALSE).

If some of the data points are not inside tri and ch.all.intri=TRUE, then the function yields an error message. If some of the data points are not inside tri and ch.all.intri=FALSE, then the function yields the closest points to edges among the data points inside tri (yields NA if there are no data points inside tri).

See also (\insertCiteceyhan:Phd-thesis,ceyhan:mcap2012;textualpcds).

Usage

fr2vertsCCvert.reg(Xp, tri, ch.all.intri = FALSE)

Arguments

Xp	A set of 2D points representing the set of data points.
tri	A 3 \times 2 matrix with each row representing a vertex of the triangle.
ch.all.intri	A logical argument (default=FALSE) to check whether all data points are inside the triangle tri. So, if it is TRUE, the function checks if all data points are inside the closure of the triangle (i.e., interior and boundary combined) else it does not.

Value

A list with the elements

txt1	Vertex labels are A=1, B=2, and C=3 (correspond to row number in Extremum Points).
txt2	A short description of the distances as "Distances from furthest points to ...".
type	Type of the extrema points
desc	A short description of the extrema points
mtitle	The "main" title for the plot of the extrema
ext	The extrema points, here, furthest points from vertices in each CC-vertex region in the triangle tri.
X	The input data, Xp, can be a matrix or data frame
num.points	The number of data points, i.e., size of Xp
supp	Support of the data points, here, it is the triangle tri for this function.
cent	The center point used for construction of edge regions.
ncent	Name of the center, cent, it is circumcenter "CC" for this function
regions	CC-Vertex regions inside the triangle, tri, provided as a list
region.names	Names of the vertex regions as "vr=1", "vr=2", and "vr=3"
region.centers	Centers of mass of the vertex regions inside tri
dist2ref	Distances from furthest points in each vertex region to the corresponding vertex

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

fr2vertsCCvert.reg.basic.tri, fr2edgesCMedge.reg.std.tri, kfr2vertsCCvert.reg.basic.tri and kfr2vertsCCvert.reg

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10  #try also n<-20

set.seed(1)
Xp<-runif.tri(n,Tr)$g

Ext<-fr2vertsCCvert.reg(Xp,Tr)
Ext
summary(Ext)
plot(Ext)

f2v<-Ext

CC<-circumcenter.tri(Tr)  #the circumcenter
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

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

plot(Tr,xlab="",asp=1,ylab="",pch=".",
main="Furthest Points in CC-Vertex Regions \n from the Vertices",
axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(Xp)
points(rbind(f2v$ext),pch=4,col=2)

txt<-rbind(Tr,CC,Ds)
xc<-txt[,1]+c(-.06,.08,.05,.12,-.1,-.1,-.09)
yc<-txt[,2]+c(.02,-.02,.05,.0,.02,.06,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)

Xp2<-rbind(Xp,c(.2,.4))
fr2vertsCCvert.reg(Xp2,Tr,ch.all.intri = FALSE)
#gives an error message if ch.all.intri = TRUE
#since not all points in the data set are in the triangle

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