cl2fVRth: 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, Dt, to face $i$ in M-vertex region $i$ for $i = 1, 2, 3, 4$ in the tetrahedron $t h = T (A, B, C, D)$ . Vertex labels are $A = 1$ , $B = 2$ , $C = 3$ , and $D = 4$ and corresponding face labels are $B C D = 1$ , $A C D = 2$ , $A B D = 3$ , and $A B C = 4$ .

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

Usage

cl2fVRth(Dt, th, M = "CM")

Value

A list with the elements

txt1: Vertex labels are $A = 1$ , $B = 2$ , $C = 3$ , and $D = 4$ (corresponds 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.
X: The input data, Dt, can be a matrix or data frame
num.points: The number of data points, i.e., size of Dt
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

Dt: A set of 3D points representing the set of data points.
th: Four 3D points, stacked row-wise, 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)
tetra<-rbind(A,B,C,D)
Cent<-"CC"  #try also "CM"

n<-10  #try also n<-20
Dt<-runif.tetra(n,tetra)$g  #try also Dt<-cbind(runif(n),runif(n),runif(n))

Ext<-cl2fVRth(Dt,tetra,Cent)
Ext
summary(Ext)
plot(Ext)

cl2fVRth(c(.5,.5,.5),tetra,Cent)

cl2fVRth(Dt,tetra,Cent)
clf<-cl2fVRth(Dt,tetra,Cent)$ext
clf

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

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

plot3D::scatter3D(Dt[,1],Dt[,2],Dt[,3], phi =0,theta=40, bty = "g",
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)

cl2fVRth(Dt,tetra,Cent)

P<-c(.1,.1,.1)
cl2fVRth(P,tetra,Cent)

dat.fr<-data.frame(a=Dt)
cl2fVRth(dat.fr,tetra,Cent)

dat.fr<-data.frame(a=tetra)
cl2fVRth(Dt,dat.fr,Cent)
# }

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