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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)