How to make a contour plot from a parametric surface in Makie?

Specific Domains Visualization
1

Hello!
Recently for a project I was wondering if there is any way to visualize the contour plot of a parametric surface in Makie. Typically, if I have the explicit expression f(x,y), I can just evaluate in a domain and use the contour (or contourf) functions. However, for my particular case consider as an example this half-sphere.

using GLMakie
phi = 0:0.01:2π
theta = 0:0.01:π/2
x = [cos(p)*sin(t) for t in theta, p in phi]
y = [sin(p)*sin(t) for t in theta, p in phi]
z = [cos(t) for t in theta, p in phi]
surface(x,y,z)

Here I have a parametric sphere, and I would like to get the circles on the x-y plane.

Any ideas on how to do this?

This is my first time asking something in the discourse, I apologize in advance if some details are missing.

2

The contour plot is associated to a surface of explicit equation, z=f(x,y). In your case you can take z=\sqrt{1-x^2-y^2}, and plot the corresponding contour plot. Due to the symmetry with respect to the plane z=0, the southern hemisphere has the same contour lines.