Plane {pcds}

The plane passing through three distinct 3D points a, b, and c

Description

An object of class "Planes". Returns the equation and z-coordinates of the plane passing through three distinct 3D points a, b, and c with x- and y-coordinates are provided in vectors x and y, respectively.

Usage

Plane(a, b, c, x, y)

Arguments

a, b, c

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

x, y

Scalars or vectors of scalars representing the x- and y-coordinates of the plane.

Value

A list with the elements

desc

A description of the plane

points

The input points a, b, and c through which the plane is passing (stacked row-wise, i.e., row 1 is point a, row 2 is point b and row 3 is point c).

x, y

The input vectors which constitutes the x- and y-coordinates of the point(s) of interest on the plane. x and y can be scalars or vectors of scalars.

z

The output vector which constitutes the z-coordinates of the point(s) of interest on the plane. If x and y are scalars, z will be a scalar and if x and y are vectors of scalars, then z needs to be a matrix of scalars, containing the z-coordinate for each pair of x and y values.

coeff

Coefficients of the plane (in the z = A x+B y+C form).

equation

Equation of the plane in long form

equation2

Equation of the plane in short form, to be inserted on the plot

Author(s)

Elvan Ceyhan

See Also

paraplane

Examples

P1<-c(1,10,3); P2<-c(1,1,3); P3<-c(3,9,12) #also try P2=c(2,2,3)

pts<-rbind(P1,P2,P3)
Plane(P1,P2,P3,.1,.2)

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
x<-seq(xr[1]-xf,xr[2]+xf,l=5)  #try also l=10, 20, or 100
y<-seq(yr[1]-yf,yr[2]+yf,l=5)  #try also l=10, 20, or 100

plP123<-Plane(P1,P2,P3,x,y)
plP123
summary(plP123)
plot(plP123,theta = 225, phi = 30, expand = 0.7, facets = FALSE, scale = TRUE)

z.grid<-plP123$z

persp(x,y,z.grid, xlab="x",ylab="y",zlab="z",
theta = -30, phi = 30, expand = 0.5, col = "lightblue",
      ltheta = 120, shade = 0.05, ticktype = "detailed")

zr<-max(z.grid)-min(z.grid)
Pts<-rbind(P1,P2,P3)+rbind(c(0,0,zr*.1),c(0,0,zr*.1),c(0,0,zr*.1))
Mn.pts<-apply(Pts,2,mean)

plot3D::persp3D(z = z.grid, x = x, y = y,theta = 225, phi = 30, expand = 0.3,
main = "Plane Crossing Points P1, P2, and P3", facets = FALSE, scale = TRUE)
#plane spanned by points P1, P2, P3
#add the defining points
plot3D::points3D(Pts[,1],Pts[,2],Pts[,3], add=TRUE)
plot3D::text3D(Pts[,1],Pts[,2],Pts[,3], c("P1","P2","P3"),add=TRUE)
plot3D::text3D(Mn.pts[1],Mn.pts[2],Mn.pts[3],plP123$equation,add=TRUE)
#plot3D::polygon3D(Pts[,1],Pts[,2],Pts[,3], add=TRUE)