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Intersections of Two Implicit Surfaces: Interactive Visualization

Intersections of Two Implicit Surfaces: Interactive Visualization
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2016-10-31 22:45
FunctionSolid GeometryParametric EquationLocusGraphing
This example demonstrates the intersection curves of two implicit surfaces in 3D space, with interactive controls to explore how the curves change. Core mathematical concepts include implicit surfaces, surface intersection, parametric curves, and stochastic processes applied to geometry. Construction highlights: uses GeoGebra commands such as ImplicitCurve to define surfaces, IntersectPath to compute intersection paths, and Polygon, Textfield, InputBox for parameter adjustment. Suitable for high school and above, useful for teaching solid geometry, calculus, or computer graphics, providing an intuitive understanding of surface intersections.

GeoGebra Commands & Parameters

  1. Textfield(f1) → InputBox1
  2. Textfield(zoom_{3D}) → InputBox2
  3. Textfield(f2) → InputBox3
  4. IntersectPath(Z_0, f2(x, y, z0) + z0) → ic2z
  5. IntersectPath(Z_0, f1(x, y, z0) + z0) → ic1z
  6. Textfield(Nn) → InputBox4
  7. Textfield(e) → InputBox5
  8. Textfield(x_{min}) → InputBox6
  9. Textfield(x_{max}) → InputBox7
  10. Textfield(y_{min}) → InputBox8
  11. Textfield(y_{max}) → InputBox9
  12. Textfield(z_{min}) → InputBox10
  13. Textfield(z_{max}) → InputBox11
  14. Textfield(v_a) → InputBox12
  15. ImplicitCurve(f2(xk, x, y)) → df2x_kyz
  16. ImplicitCurve(f01(xk, x, y)) → df01x_kyz
  17. ImplicitCurve(f1(xk, x, y)) → df1x_kyza
  18. ImplicitCurve(f1(x, yk, y)) → rf1xy_kz
  19. ImplicitCurve(f2(x, yk, y)) → rf2xy_kz
  20. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, g, j, k, l
  21. Textfield(α) → InputBox13
  22. ImplicitCurve(f01(x, yk, y)) → df01xykz