cl2edgesCCvert.reg: The closest points in a data set to edges in each CC-vertex...

In pcds: Proximity Catch Digraphs and Their Applications

The closest points in a data set to edges in each CC-vertex region in a triangle

Description

An object of class "Extrema". Returns the closest data points among the data set, Xp, to edge j in CC-vertex region j for j=1,2,3 in the triangle, tri=T(A,B,C), where CC stands for circumcenter. Vertex labels are A=1, B=2, and C=3, and corresponding edge labels are BC=1, AC=2, and AB=3. Function yields NA if there are no data points in a CC-vertex region.

See also (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010;textualpcds).

Usage

cl2edgesCCvert.reg(Xp, tri)

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.

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 to Edges in the Respective CC-Vertex Regions".
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, closest points to edges in the respective vertex region.
ind.ext	Indices of the extrema points,ext.
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 tri
cent	The center point used for construction of vertex regions
ncent	Name of the center, cent, it is "CC" for this function
regions	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 of closest points in the vertex regions to corresponding edges

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

cl2edges.vert.reg.basic.tri, cl2edgesCMvert.reg, cl2edgesMvert.reg, and cl2edges.std.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);

n<-20  #try also n<-100
set.seed(1)
Xp<-runif.tri(n,Tr)$g

Ext<-cl2edgesCCvert.reg(Xp,Tr)
Ext
summary(Ext)
plot(Ext)

cl2e<-Ext

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

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

plot(Tr,asp=1,pch=".",xlab="",ylab="",
main="Closest Points in CC-Vertex Regions \n to the Opposite Edges",
axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)

xc<-Tr[,1]+c(-.02,.02,.02)
yc<-Tr[,2]+c(.02,.02,.04)
txt.str<-c("A","B","C")
text(xc,yc,txt.str)

points(Xp,pch=1,col=1)
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(cl2e$ext,pch=3,col=2)

txt<-rbind(CC,Ds)
xc<-txt[,1]+c(-.04,.04,-.03,0)
yc<-txt[,2]+c(-.05,.04,.06,-.08)
txt.str<-c("CC","D1","D2","D3")
text(xc,yc,txt.str)

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