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Sphere Animation

Sphere Animation
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2014-12-03 03:33
Solid GeometryParametric EquationGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates a sphere animation. It involves concepts of spherical geometry and parametric equations. Using GeoGebra commands such as Surface, Sphere, and Sequence, a dynamic sphere model can be constructed. Suitable for high school and above students or teachers for teaching and learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(Line[(-1, -2, 0), (-1, -2, 1)]) → B
  2. Point(Line[(0, -2, 0), (0, -2, 1)]) → C
  3. Point(Line[(1, -2, 0), (1, -2, 1)]) → D
  4. Point(Line[(-2, -1, 0), (-2, -1, 1)]) → F
  5. Point(Line[(-2, 0, 0), (-2, 0, 1)]) → G
  6. Point(Line[(-2, 1, 0), (-2, 1, 1)]) → H
  7. FitPoly({(x(A), z(A)), (x(B), z(B)), (x(C), z(C)), (x(D), z(D)), (x(E), z(E))}, 4) → f
  8. FitPoly({(y(A), z(A)), (y(F), z(F)), (y(G), z(G)), (y(H), z(H)), (y(I), z(I))}, 4) → g
  9. CurveCartesian(t, -2, f(t), t, -2, 2) → a
  10. CurveCartesian(-2, t, g(t), t, -2, 2) → b
  11. Point(Line[(-1, 2, 0), (-1, 2, 1)]) → J
  12. Point(Line[(0, 2, 0), (0, 2, 1)]) → K
  13. Point(Line[(1, 2, 0), (1, 2, 1)]) → L
  14. FitPoly({(x(I), z(I)), (x(J), z(J)), (x(K), z(K)), (x(L), z(L)), (x(M), z(M))}, 4) → f2
  15. CurveCartesian(t, 2, f2(t), t, -2, 2) → d
  16. Point(Line[(2, -1, 0), (2, -1, 1)]) → N
  17. Point(Line[(2, 0, 0), (2, 0, 1)]) → O
  18. Point(Line[(2, 1, 0), (2, 1, 1)]) → P
  19. FitPoly({(y(E), z(E)), (y(N), z(N)), (y(O), z(O)), (y(P), z(P)), (y(M), z(M))}, 4) → g2
  20. CurveCartesian(2, t, g2(t), t, -2, 2) → e
  21. Surface(u, v, ((1 - (v + 2) / 4) * f(u)) + ((v + 2) / 4 * f2(u)) + ((1 - (u + 2) / 4) * g(v)) + ((u + 2) / 4 * g2(v)), u, -2, 2, v, -2, 2) → c
  22. Plane(Q', Plx, Ply) → i
  23. OrthogonalLine(Q', i) → j
  24. Intersect(j, Sphere[Q', r]) → S, T
  25. Sphere(T, r) → k_1
  26. Sequence(CurveCartesian[u, v, ((1 - (v + 2) / 4) * f(u)) + ((v + 2) / 4 * f2(u)) + ((1 - (u + 2) / 4) * g(v)) + ((u + 2) / 4 * g2(v)), u, -2, 2], v, -2, 2, 4 / n) → liste1
  27. Sequence(CurveCartesian[u, v, ((1 - (v + 2) / 4) * f(u)) + ((v + 2) / 4 * f2(u)) + ((1 - (u + 2) / 4) * g(v)) + ((u + 2) / 4 * g2(v)), v, -2, 2], u, -2, 2, 4 / n) → liste2

AI Drawing Prompt Reference

Create an animation of a sphere to demonstrate its dynamic changes. First, create several points on lines at different positions, then fit four polynomial curves based on these points. Next, generate two curves using these curves, and construct a surface from them. Finally, create multiple curves on the surface to form the dynamic effect of the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.