cl2faces.vert.reg.tetra: The closest points among a data set in the vertex regions to the respective faces in a tetrahedron

Description

An object of class "Extrema". Returns the closest data points among the data set, Xp, to face \(i\) in M-vertex region \(i\) for \(i=1,2,3,4\) in the tetrahedron \(th=T(A,B,C,D)\). Vertex labels are \(A=1\), \(B=2\), \(C=3\), and \(D=4\) and corresponding face labels are \(BCD=1\), \(ACD=2\), \(ABD=3\), and \(ABC=4\).

Vertex regions are based on center M which can be the center of mass ("CM") or circumcenter ("CC") of th.

Usage

cl2faces.vert.reg.tetra(Xp, th, M = "CM")

Value

A list with the elements

txt1: Vertex labels are \(A=1\), \(B=2\), \(C=3\), and \(D=4\) (correspond to row number in Extremum Points).
txt2: A short description of the distances as "Distances from Closest Points to Faces ...".
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 faces in the respective vertex region.
ind.ext: The data indices of 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 th
cent: The center point used for construction of vertex regions, it is circumcenter of center of mass for this function
ncent: Name of the center, it is circumcenter "CC" or center of mass "CM" for this function.
regions: Vertex regions inside the tetrahedron th provided as a list.
region.names: Names of the vertex regions as "vr=1","vr=2","vr=3","vr=4"
region.centers: Centers of mass of the vertex regions inside th.
dist2ref: Distances from closest points in each vertex region to the corresponding face.

Arguments

Xp: A set of 3D points representing the set of data points.
th: A \(4 \times 3\) matrix with each row representing a vertex of the tetrahedron.
M: The center to be used in the construction of the vertex regions in the tetrahedron, th. Currently it only takes "CC" for circumcenter and "CM" for center of mass; default="CM".

Author

Elvan Ceyhan

Examples

Run this code

# \donttest{
A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0);
D<-c(1/2,sqrt(3)/6,sqrt(6)/3)
set.seed(1)
tetra<-rbind(A,B,C,D)+matrix(runif(12,-.25,.25),ncol=3)
n<-10  #try also n<-20
Cent<-"CC"  #try also "CM"

n<-20  #try also n<-100
Xp<-runif.tetra(n,tetra)$g  #try also Xp<-cbind(runif(n),runif(n),runif(n))

Ext<-cl2faces.vert.reg.tetra(Xp,tetra,Cent)
Ext
summary(Ext)
plot(Ext)

clf<-Ext$ext

if (Cent=="CC") {M<-circumcenter.tetra(tetra)}
if (Cent=="CM") {M<-apply(tetra,2,mean)}

Xlim<-range(tetra[,1],Xp[,1],M[1])
Ylim<-range(tetra[,2],Xp[,2],M[2])
Zlim<-range(tetra[,3],Xp[,3],M[3])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
zd<-Zlim[2]-Zlim[1]

plot3D::scatter3D(Xp[,1],Xp[,2],Xp[,3], phi =0,theta=40, bty = "g",
main="Closest Pointsin CC-Vertex Regions \n to the Opposite Faces",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05), zlim=Zlim+zd*c(-.05,.05),
          pch = 20, cex = 1, ticktype = "detailed")
#add the vertices of the tetrahedron
plot3D::points3D(tetra[,1],tetra[,2],tetra[,3], add=TRUE)
L<-rbind(A,A,A,B,B,C); R<-rbind(B,C,D,C,D,D)
plot3D::segments3D(L[,1], L[,2], L[,3], R[,1], R[,2],R[,3], add=TRUE,lwd=2)
plot3D::points3D(clf[,1],clf[,2],clf[,3], pch=4,col="red", add=TRUE)

plot3D::text3D(tetra[,1],tetra[,2],tetra[,3],
labels=c("A","B","C","D"), add=TRUE)

#for center of mass use #Cent<-apply(tetra,2,mean)
D1<-(A+B)/2; D2<-(A+C)/2; D3<-(A+D)/2;
D4<-(B+C)/2; D5<-(B+D)/2; D6<-(C+D)/2;
L<-rbind(D1,D2,D3,D4,D5,D6); R<-rbind(M,M,M,M,M,M)
plot3D::segments3D(L[,1], L[,2], L[,3], R[,1], R[,2],R[,3], add=TRUE,lty=2)
# }