paraline3D: The line crossing the 3D point `p` and parallel to line joining 3D points `a` and `b`

Description

An object of class "Lines3D". Returns the equation, \(x\)-, \(y\)-, and \(z\)-coordinates of the line crossing 3D point p and parallel to the line joining 3D points a and b (i.e., the line is in the direction of vector b-a) with the parameter t being provided in vector t.

Usage

paraline3D(p, a, b, t)

Value

A list with the elements

desc: A description of the line
mtitle: The "main" title for the plot of the line
points: The input points that determine the line to which the line crossing point p would be parallel.
pnames: The names of the input points that determine the line to which the line crossing point p would be parallel.
vecs: The points p, a, and b stacked row-wise in this order.
vec.names: The names of the points p, a, and b.
x,y,z: The \(x\)-, \(y\)-, and \(z\)-coordinates of the point(s) of interest on the line parallel to the line determined by points a and b.
tsq: The scalar or the vector of the parameter in defining each coordinate of the line for the form: \(x=p_0 + A t\), \(y=y_0 + B t\), and \(z=z_0 + C t\) where \(p=(p_0,y_0,z_0)\) and \(b-a=(A,B,C)\).
equation: Equation of the line passing through point p and parallel to the line joining points a and b (i.e., in the direction of the vector b-a). The line equation is in the form: \(x=p_0 + A t\), \(y=y_0 + B t\), and \(z=z_0 + C t\) where \(p=(p_0,y_0,z_0)\) and \(b-a=(A,B,C)\).

Arguments

p: A 3D point through which the straight line passes.
a, b: 3D points which determine the straight line to which the line passing through point p would be parallel (i.e., \(b-a\) determines the direction of the straight line passing through p).
t: A scalar or a vector of scalars representing the parameter of the coordinates of the line (for the form: \(x=p_0 + A t\), \(y=y_0 + B t\), and \(z=z_0 + C t\) where \(p=(p_0,y_0,z_0)\) and \(b-a=(A,B,C)\)).

Author

Elvan Ceyhan

Examples

Run this code

# \donttest{
P<-c(1,10,4); Q<-c(1,1,3); R<-c(3,9,12)

vecs<-rbind(P,R-Q)
pts<-rbind(P,Q,R)
paraline3D(P,Q,R,.1)

tr<-range(pts,vecs);
tf<-(tr[2]-tr[1])*.1
#how far to go at the lower and upper ends in the x-coordinate
tsq<-seq(-tf*10-tf,tf*10+tf,l=5)  #try also l=10, 20, or 100

pln3D<-paraline3D(P,Q,R,tsq)
pln3D
summary(pln3D)
plot(pln3D)

x<-pln3D$x
y<-pln3D$y
z<-pln3D$z

zr<-range(z)
zf<-(zr[2]-zr[1])*.2
Qv<-(R-Q)*tf*5

Xlim<-range(x,pts[,1])
Ylim<-range(y,pts[,2])
Zlim<-range(z,pts[,3])

xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
zd<-Zlim[2]-Zlim[1]

Dr<-P+min(tsq)*(R-Q)

plot3D::lines3D(x, y, z, phi = 0, bty = "g",
main="Line Crossing P \n in the direction of R-Q",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05),
zlim=Zlim+zd*c(-.1,.1)+c(-zf,zf),
        pch = 20, cex = 2, ticktype = "detailed")
plot3D::arrows3D(Dr[1],Dr[2],Dr[3]+zf,Dr[1]+Qv[1],
Dr[2]+Qv[2],Dr[3]+zf+Qv[3], add=TRUE)
plot3D::points3D(pts[,1],pts[,2],pts[,3],add=TRUE)
plot3D::text3D(pts[,1],pts[,2],pts[,3],labels=c("P","Q","R"),add=TRUE)
plot3D::arrows3D(P[1],P[2],P[3]-2*zf,P[1],P[2],P[3],lty=2, add=TRUE)
plot3D::text3D(P[1],P[2],P[3]-2*zf,labels="initial point",add=TRUE)
plot3D::arrows3D(Dr[1]+Qv[1]/2,Dr[2]+Qv[2]/2,
Dr[3]+3*zf+Qv[3]/2,Dr[1]+Qv[1]/2,
Dr[2]+Qv[2]/2,Dr[3]+zf+Qv[3]/2,lty=2, add=TRUE)
plot3D::text3D(Dr[1]+Qv[1]/2,Dr[2]+Qv[2]/2,Dr[3]+3*zf+Qv[3]/2,
labels="direction vector",add=TRUE)
plot3D::text3D(Dr[1]+Qv[1]/2,Dr[2]+Qv[2]/2,
Dr[3]+zf+Qv[3]/2,labels="R-Q",add=TRUE)
# }