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Quadric Surfaces by Osvaldo Choucair Vaz da Silva

Quadric Surfaces by Osvaldo Choucair Vaz da Silva
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2018-08-20 23:25
FunctionCoordinate GeometrySolid Geometry
This example demonstrates various quadric surfaces such as ellipsoids, hyperboloids, and paraboloids. By modifying R Vozzo's original work, the specific equations for each quadric surface are added. It uses commands like IntersectPath for construction, suitable for high school or university-level solid geometry.

GeoGebra Commands & Parameters

  1. IntersectPath(l, d) → q
  2. IntersectPath(n, d) → c_1
  3. IntersectPath(p, d) → d_1
  4. IntersectPath(l, f) → e_1
  5. IntersectPath(n, f) → f_1
  6. IntersectPath(p, f) → g_1
  7. IntersectPath(n, e) → h_1
  8. IntersectPath(p, e) → k_1
  9. IntersectPath(l, e) → p_1
  10. IntersectPath(n, j) → q_1
  11. IntersectPath(p, j) → r_1
  12. IntersectPath(l, j) → s_1
  13. IntersectPath(n, g) → t_1
  14. IntersectPath(p, g) → c_2
  15. IntersectPath(l, g) → d_2
  16. IntersectPath(n, h) → e_2
  17. IntersectPath(p, h) → f_2
  18. IntersectPath(l, h) → g_2

AI Drawing Prompt Reference

Create a 3D coordinate system showing several quadric surfaces, including ellipsoids, hyperboloids, and paraboloids. Use three mutually perpendicular planes (like coordinate planes) to intersect these surfaces, producing intersection curves that appear as ellipses, hyperbolas, or parabolas. Construction order: first draw the surfaces, then place the three cutting planes, then compute and highlight the intersection curves for each plane with each surface. The overall figure should clearly show the spatial relationships between surfaces and sections, suitable for solid geometry teaching.
The prompt above was compiled from the original drawing commands and is for reference only.