pcds (version 0.1.2)

int.line.plane: The point of intersection of a line and a plane

Description

Returns the point of the intersection of the line determined by the 3D points \(x_1\) and \(x_2\) and the plane spanned by 3D points x3, x4, and x5.

Usage

int.line.plane(x1, x2, x3, x4, x5)

Arguments

x1, x2

3D points that determine the straight line (i.e., through which the straight line passes).

x3, x4, x5

3D points that determine the plane (i.e., through which the plane passes).

Value

The coordinates of the point of intersection the line determined by the 3D points \(x_1\) and \(x_2\) and the plane determined by 3D points x3, x4, and x5.

See Also

int.2lines and int.circ.line

Examples

# NOT RUN {
L1<-c(2,4,6); L2<-c(1,3,5); A<-c(1,10,3); B<-c(1,1,3); C<-c(3,9,12)

Pint<-int.line.plane(L1,L2,A,B,C)
Pint
pts<-rbind(L1,L2,A,B,C,Pint)

tr<-max(Dist(L1,L2),Dist(L1,Pint),Dist(L2,Pint))
tf<-tr*1.1 #how far to go at the lower and upper ends in the x-coordinate
tsq<-seq(-tf,tf,l=20)  #try also l=100

lnAB3D<-Line3D(L1,L2,tsq)
xl<-lnAB3D$x
yl<-lnAB3D$y
zl<-lnAB3D$z

xr<-range(pts[,1]); yr<-range(pts[,2])
xf<-(xr[2]-xr[1])*.1 #how far to go at the lower and upper ends in the x-coordinate
yf<-(yr[2]-yr[1])*.1 #how far to go at the lower and upper ends in the y-coordinate
xp<-seq(xr[1]-xf,xr[2]+xf,l=20)  #try also l=100
yp<-seq(yr[1]-yf,yr[2]+yf,l=20)  #try also l=100

plABC<-Plane(A,B,C,xp,yp)
z.grid<-plABC$z

res<-persp(xp,yp,z.grid, xlab="x",ylab="y",zlab="z",theta = -30, phi = 30, expand = 0.5,
col = "lightblue", ltheta = 120, shade = 0.05, ticktype = "detailed")
lines (trans3d(xl, yl, zl, pmat = res), col = 3)

Xlim<-range(xl,pts[,1])
Ylim<-range(yl,pts[,2])
Zlim<-range(zl,pts[,3])

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

plot3D::persp3D(z = z.grid, x = xp, y = yp, theta =225, phi = 30, ticktype = "detailed"
        ,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05),zlim=Zlim+zd*c(-.1,.1))
        #plane spanned by points A, B, C
#add the defining points
plot3D::points3D(pts[,1],pts[,2],pts[,3], pch = ".", col = "black", bty = "f", cex = 5,add=TRUE)
plot3D::points3D(Pint[1],Pint[2],Pint[3], pch = "*", col = "red", bty = "f", cex = 5,add=TRUE)
plot3D::lines3D(xl, yl, zl, bty = "g", cex = 2, ticktype = "detailed",add=TRUE)
# }
# NOT RUN {
# }