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Special Spheroid Locus Demonstration

Special Spheroid Locus Demonstration
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2016-08-27 10:37
Solid GeometryGeometric ConstructionLocus
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Multivariable Calculus Quadratic Surfaces
This example demonstrates the locus of a special spheroid. Key mathematical concepts include the rotation of spheroids, locus, and solid geometry. Using GeoGebra commands such as PointIn, IntersectPath, and Rotate, the formation of the locus is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. PointIn(d) → A
  2. IntersectPath(z = 0, d) → e
  3. Max({MajorAxis, MinorAxis, c}) → max
  4. Focus(e) → B, C
  5. Vertex(e) → D, E, F, G
  6. Dilate(B, If[0 < Animate ≤ 1, 1 - Animate, 0], A) → B'
  7. Segment(B, B') → i
  8. Dilate(C, If[0 < Animate ≤ 1, 1 - Animate, 0], A) → C'
  9. Segment(C, C') → j
  10. Vertex(f) → H, I, J, K
  11. Vertex(g) → L, M, N, O
  12. Dilate(B, If[1.5 < Animate ≤ 2.5, 2.5 - Animate, 0], D) → B'_1
  13. Vector(B, B'_1) → u
  14. Translate(B, u) → B'_2
  15. Translate(B', u) → B''
  16. Segment(B'_2, B'') → i'
  17. OrthogonalLine(B'', k) → l
  18. Point(e) → R
  19. Sphere(D, B'') → m
  20. IntersectPath(z = 0, m) → p
  21. Intersect(p, e) → P, Q, ,
  22. Angle(P, D, B'') → α
  23. Rotate(B'_2, If[2.5 < Animate ≤ 3.5, ((-(Animate - 2.5)) * α), (-α)], D) → S
  24. Plane(B'', D, P) → n
  25. Rotate(B'_2, If[2.5 < Animate ≤ 3.5, ((-(Animate - 2.5)) * α), (-α)], D, n) → T
  26. Rotate(B'', If[2.5 < Animate ≤ 3.5, ((-(Animate - 2.5)) * α), (-α)], D, n) → B'''
  27. Segment(T, B''') → i''
  28. Angle(B''', D, B) → β
  29. Rotate(T, If[3.5 < Animate ≤ 4.5, ((Animate - 3.5) * β), β], D) → T'
  30. Rotate(B''', If[3.5 < Animate ≤ 4.5, ((Animate - 3.5) * β), β], D) → U
  31. Segment(T', U) → i'''
  32. Dilate(C, If[4.5 < Animate ≤ 5.5, 5.5 - Animate, 0], E) → C'_1
  33. Vector(C, C'_1) → v
  34. Translate(C, v) → C'_2
  35. Translate(C', v) → C''
  36. Segment(C'_2, C'') → j'
  37. Sphere(E, C'') → o
  38. IntersectPath(z = 0, o) → q
  39. Intersect(q, e) → V, W, ,
  40. Angle(W, E, C'') → γ
  41. Plane(E, C'', W) → r
  42. Rotate(C'_2, If[5.5 < Animate ≤ 6.5, ((Animate - 5.5) * γ), γ], E, r) → Z
  43. Rotate(C'', If[5.5 < Animate ≤ 6.5, ((Animate - 5.5) * γ), γ], E, r) → C'''
  44. Segment(Z, C''') → j''
  45. Angle(W, E, D) → δ
  46. Rotate(Z, If[6.5 < Animate ≤ 7.5, ((Animate - 6.5) * δ), δ], E) → Z'
  47. Rotate(C''', If[6.5 < Animate ≤ 7.5, ((Animate - 6.5) * δ), δ], E) → A_1
  48. Segment(Z', A_1) → j'''
  49. Distance(B, A) → s
  50. Circle(D, s, xOyPlane) → t
  51. Segment(D, E) → f_1
  52. Intersect(f_1, xAxis) → B_1
  53. Intersect(f_1, t) → C_1, E_1
  54. Segment(D, C_1) → g_1
  55. Segment(C_1, E) → h_1
  56. Dilate(D, If[0 < Animate ≤ 1, 1 - Animate, 0], C_1) → D'
  57. Segment(D, D') → i_1
  58. Dilate(C_1, If[1 < Animate ≤ 2, 2 - Animate, 0], E) → D_1
  59. Segment(C_1, D_1) → j_1
  60. Rotate(B''', If[3.5 < Animate ≤ 4.5, ((-(Animate - 3.5)) * β), (-β)], D) → F_1
  61. Segment(D, F_1) → k_1

AI Drawing Prompt Reference

Draw a special spheroid locus by first creating a point A on a plane, then creating points B and C on the spheroid. Use rotation and scaling to dynamically generate trajectory points P and Q, and create trajectory lines i and j. Finally, use rotation and translation to generate trajectory lines i', i'', and i''', as well as j', j'', and j''', forming a dynamic spheroid locus.
The prompt above was compiled from the original drawing commands and is for reference only.