How to plot 3d parametric equations in R?

Question

From the parametric equations on wiki page ( http://en.wikipedia.org/wiki/Parametric_equation ), I can plot 2d equations as follows:

#for a circle: 
x = seq(-pi, pi, length.out=30)
plot(sin(x),cos(x))

# for a star: 
a=10; b=10/1.8
x=seq(-50,50,length.out=500)
plot((a-b)*cos(x)+b*cos(x*((a/b)-1)), (a-b)*sin(x)-b*sin(x*((a/b)-1)), ylim=range(-13,13))

How can I plot 3d equations on a 3d plot of a Helix given by equations:

x=a*cos(t)
y=a*sin(t)
z=b*t

From searching I found that the 3d plotting functions take either a matrix or x,y,z values but not math curve functions.

Answer 1

You can plot 3D equations like you did the 2D ones.

library(lattice)
t<-seq(-2*pi, 2*pi, length.out=200)
cloud(z~x+y,data.frame(x=3*cos(t),y=3*sin(t), z=2*t))

So yes, you can't supply a raw function directly, but you can easily calculate points to plot based on those functions. Let me know if you had something else in mind.

Here's a two-parameter torus

t <- seq(0, 2*pi, length.out=50); 
u <- seq(0, 2*pi, length.out=50); 
tu<-expand.grid(t=t,u=u)
R <- 6; 
r <- 3; 
tu <- transform(tu, 
    x = cos(t)*(R+r*cos(u)), 
    y = sin(t)*(R+r*cos(u)),
    z = r*sin(u)
)

rr<-c(-10,10)
cloud(z~x+y, tu, xlim=rr, ylim=rr, zlim=rr, screen=list(y=20));

Actually, I just realized wireframe is better, just took me a bit longer to figure out the syntax.

xm<-outer(t,u,function(t, u)cos(t)*(R+r*cos(u)))
ym<-outer(t,u,function(t, u)sin(t)*(R+r*cos(u)))
zm<-outer(t,u,function(t, u) r*sin(u))

rr<-c(-10,10)
wireframe(zm~xm+ym, xlim=rr, ylim=rr, zlim=rr, screen=list(y=30))

More details found on the ?cloud help page

Answer 2

With plotly:

library(plotly)

t <- seq(-2*pi, 2*pi, length.out=200)
dat <- data.frame(x=3*cos(t), y=3*sin(t), z=2*t)

plot_ly(dat, x = ~x, y = ~y, z = ~z, type = 'scatter3d', mode = 'lines',
        line = list(width = 4))