Intersection of Sphere & Plane: How to obtain the parametric equations?
Applying matrix diagonalisation in the classroom with GeoGebra: parametrising the intersection of a sphere and plane
Bradley Graeme Welch & Juan Carlos Ponce Campuzano
https://www.tandfonline.com/doi/full/10.1080/0020739X.2023.2233513
2024 Teaching and Learning Seminar at UNSW (May 2024):
https://slides.com/jcponce/tl-seminar/fullscreen
GeoGebra Script
# Parameters
# Centre of sphere & radius
x_0 = Slider(-4, 4, 0.1, 1, 120)
y_0 = Slider(-4, 4, 0.1, 1, 120)
z_0 = Slider(-4, 4, 0.1, 1, 120)
R = Slider(0.1, 4, 0.1, 1, 120)
# Plane
A = Slider(-4, 4, 0.1, 1, 120)
B = Slider(-4, 4, 0.1, 1, 120)
C = Slider(-4, 4, 0.1, 1, 120)
D = Slider(-4, 4, 0.1, 1, 120)
# Define sphere
S: (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = R^2
# Define plane
PI: A * x + B * y + C * z = D
# Signed distance
rho = (A * x_0 + B * y_0 + C * z_0 - D) / sqrt(A^2 + B^2 + C^2)
# Intersection curve
intCur = Intersect(S, PI)
Another approach by mathmaggic
https://www.geogebra.org/m/uxbe4yrn