plot level lines (2 circumferences) on a 3d plot

Question

I'm trying to plot the two circumferences with dimensions xy together with the 3d plot and colour the intersection of the two circles, how can I do that?

# objective function
x <- seq(-1,1,.1)
y <- seq(-1,1,.1)
z <- x^2 + y^2

library(scatterplot3d)
library(plotrix)
scatterplot3d(x,y,z,pch=19,color="royalblue4")
draw.circle (1,1,1)
draw.circle (1,-1,1)

Answer 1

I'm not really into mathematic stuff, but I'll post as answer because it might be of use and, also, is too big for a comment. Excuse any ignorance of mine, though, if I post nonsense.

#your data
library(scatterplot3d)
x <- seq(-1,1,.1)
y <- seq(-1,1,.1)
z <- x^2 + y^2

ang = 60 #angle of the 3D plot. experiment with different values

#your 3D plot, with extended xx', yy' limits
sp3d <- scatterplot3d(x, y, z, pch=19, color="royalblue4", 
           xlim = c(-1, 3), ylim = c(-3, 3), angle = ang)

#to use parametric equations of circles
f <- seq(-2*pi, 2*pi, 0.1)

#circle1
sp3d$points(x = 1 + 1*cos(f), y = 1 + 1*sin(f), z = rep(0, length(f)), type = "l")
#circle2
sp3d$points(x = 1 + 1*cos(f), y = -1 + 1*sin(f), z = rep(0, length(f)), type = "l")

The plot is: