circumcenter.tetra {pcds}

Circumcenter of a general tetrahedron

Description

Returns the circumcenter a given tetrahedron th with vertices stacked row-wise.

Usage

circumcenter.tetra(th)

Arguments

th

A 4 \times 3 matrix with each row representing a vertex of the tetrahedron.

Value

circumcenter of the tetrahedron th

Author(s)

Elvan Ceyhan

See Also

circumcenter.tri

Examples

set.seed(123)
A<-c(0,0,0)+runif(3,-.2,.2);
B<-c(1,0,0)+runif(3,-.2,.2);
C<-c(1/2,sqrt(3)/2,0)+runif(3,-.2,.2);
D<-c(1/2,sqrt(3)/6,sqrt(6)/3)+runif(3,-.2,.2);
tetra<-rbind(A,B,C,D)

CC<-circumcenter.tetra(tetra)
CC

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

plot3D::scatter3D(tetra[,1],tetra[,2],tetra[,3], phi =0,theta=40, bty = "g",
main="Illustration of the Circumcenter\n in a Tetrahedron",
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(CC[1],CC[2],CC[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::text3D(tetra[,1],tetra[,2],tetra[,3],
labels=c("A","B","C","D"), add=TRUE)

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<-matrix(rep(CC,6),byrow = TRUE,ncol=3)
plot3D::segments3D(L[,1], L[,2], L[,3], R[,1], R[,2],R[,3], add=TRUE,lty = 2)

plot3D::text3D(CC[1],CC[2],CC[3], labels="CC", add=TRUE)