perpline2plane {pcds}

The line crossing the 3D point p and perpendicular to the plane spanned by 3D points a, b, and c

Description

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

Usage

perpline2plane(p, a, b, c, t)

Arguments

p

A 3D point through which the straight line passes.

a, b, c

3D points which determine the plane to which the line passing through point p would be perpendicular (i.e., the normal vector of this plane 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 normal vector=(A,B,C)).

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 and plane, line crosses point p and plane is determined by 3D points a, b, and c.

pnames

The names of the input points that determine the line and plane; line would be perpendicular to the plane.

vecs

The point p and normal vector.

vec.names

The names of the point p and the second entry is "normal vector".

x, y, z

The x-, y-, and z-coordinates of the point(s) of interest on the line perpendicular to the plane determined by points a, b, and c.

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 normal vector=(A,B,C).

equation

Equation of the line passing through point p and perpendicular to the plane determined by points a, b, and c (i.e., line is in the direction of the normal vector N of the plane). 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 normal vector=(A,B,C).

Author(s)

Elvan Ceyhan

See Also

Line3D, paraline3D, and perpline

Examples

P<-c(1,1,1); Q<-c(1,10,4); R<-c(1,1,3); S<-c(3,9,12)

cf<-as.numeric(Plane(Q,R,S,1,1)$coeff)
a<-cf[1]; b<-cf[2]; c<- -1;

vecs<-rbind(Q,c(a,b,c))
pts<-rbind(P,Q,R,S)
perpline2plane(P,Q,R,S,.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

pln2pl<-perpline2plane(P,Q,R,S,tsq)
pln2pl
summary(pln2pl)
plot(pln2pl,theta = 225, phi = 30, expand = 0.7,
facets = FALSE, scale = TRUE)

xc<-pln2pl$x
yc<-pln2pl$y
zc<-pln2pl$z

zr<-range(zc)
zf<-(zr[2]-zr[1])*.2
Rv<- -c(a,b,c)*zf*5

Dr<-(Q+R+S)/3

pts2<-rbind(Q,R,S)
xr<-range(pts2[,1],xc); yr<-range(pts2[,2],yc)
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
xs<-seq(xr[1]-xf,xr[2]+xf,l=5)  #try also l=10, 20, or 100
ys<-seq(yr[1]-yf,yr[2]+yf,l=5)  #try also l=10, 20, or 100

plQRS<-Plane(Q,R,S,xs,ys)
z.grid<-plQRS$z

Xlim<-range(xc,xs,pts[,1])
Ylim<-range(yc,ys,pts[,2])
Zlim<-range(zc,z.grid,pts[,3])

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

plot3D::persp3D(z = z.grid, x = xs, y = ys, theta =225, phi = 30,
main="Line Crossing P and \n Perpendicular to the Plane Defined by Q, R, S",
col="lightblue", ticktype = "detailed",
        xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05),
        zlim=Zlim+zd*c(-.05,.05))
        #plane spanned by points Q, R, S
plot3D::lines3D(xc, yc, zc, bty = "g",pch = 20, cex = 2,col="red",
ticktype = "detailed",add=TRUE)
plot3D::arrows3D(Dr[1],Dr[2],Dr[3],Dr[1]+Rv[1],Dr[2]+Rv[2],
Dr[3]+Rv[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","S"),add=TRUE)
plot3D::arrows3D(P[1],P[2],P[3]-zf,P[1],P[2],P[3],lty=2, add=TRUE)
plot3D::text3D(P[1],P[2],P[3]-zf,labels="initial point",add=TRUE)
plot3D::text3D(P[1],P[2],P[3]+zf/2,labels="P",add=TRUE)
plot3D::arrows3D(Dr[1],Dr[2],Dr[3],Dr[1]+Rv[1]/2,Dr[2]+Rv[2]/2,
Dr[3]+Rv[3]/2,lty=2, add=TRUE)
plot3D::text3D(Dr[1]+Rv[1]/2,Dr[2]+Rv[2]/2,Dr[3]+Rv[3]/2,
labels="normal vector",add=TRUE)