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Luminous Spherical Projection

Luminous Spherical Projection
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2020-12-18 01:03
FunctionCoordinate GeometrySolid Geometry
This example demonstrates the projection phenomenon on a sphere. It involves concepts such as spheres, quadrilaterals, and exponential functions. Using GeoGebra commands like Function, Sequence, Sphere, Line, etc., a dynamic spherical projection effect can be constructed. Suitable for high school math education or research.

GeoGebra Commands & Parameters

  1. Function({0, 6.28319, 0, 0, 1, 1, 1, 0, 0}) → f
  2. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste1
  3. Sphere(O, R) → a
  4. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), y(O) + ((R * sin(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), z(O) + (R * sin(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste2
  5. Line(O, zAxis) → g
  6. Point(g) → D
  7. Segment(C, D) → h_{1}
  8. Point(h_{1}) → E
  9. Sequence(CurveCartesian[x(C) + ((((2 * R) + (0.5 * h)) * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(C) + ((((2 * R) + (0.5 * h)) * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(C) - 0, t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → l1
  10. Circle((0, 0, 0), (2 * R) + (0.5 * h), zAxis) → c
  11. Circle((0, 0, 0), A1, zAxis) → B1
  12. Circle((0, 0, 0), A2, zAxis) → B2
  13. Circle((0, 0, 0), A3, zAxis) → B3
  14. Circle((0, 0, 0), A4, zAxis) → B4
  15. Circle((0, 0, 0), A5, zAxis) → B5
  16. Circle((0, 0, 0), A6, zAxis) → B6
  17. Circle((0, 0, 0), A7, zAxis) → B7
  18. Circle((0, 0, 0), A8, zAxis) → B8
  19. Circle((0, 0, 0), A9, zAxis) → B9
  20. Circle((0, 0, 0), A10, zAxis) → B10
  21. Circle((0, 0, 0), A11, zAxis) → B11
  22. Circle((0, 0, 0), A12, zAxis) → B12
  23. Circle((0, 0, 0), A13, zAxis) → B13
  24. Circle((0, 0, 0), A14, zAxis) → B14
  25. Circle((0, 0, 0), A15, zAxis) → B15
  26. Circle((0, 0, 0), A16, zAxis) → B16
  27. Circle((0, 0, 0), A17, zAxis) → B17
  28. Circle((0, 0, 0), A18, zAxis) → B18
  29. Circle((0, 0, 0), A19, zAxis) → B19
  30. Circle((0, 0, 0), A20, zAxis) → B20
  31. Circle((0, 0, 0), A21, zAxis) → B21
  32. Circle((0, 0, 0), A22, zAxis) → B22
  33. Circle((0, 0, 0), A23, zAxis) → B23
  34. Circle((0, 0, 0), A24, zAxis) → B24
  35. Circle((0, 0, 0), A25, zAxis) → B25
  36. Circle((0, 0, 0), A26, zAxis) → B26
  37. Circle((0, 0, 0), A27, zAxis) → B27
  38. Circle((0, 0, 0), A28, zAxis) → B28
  39. Circle((0, 0, 0), A29, zAxis) → B29
  40. Circle((0, 0, 0), A30, zAxis) → B30
  41. Circle((0, 0, 0), A31, zAxis) → B31
  42. Circle((0, 0, 0), A32, zAxis) → B32
  43. Circle((0, 0, 0), A33, zAxis) → B33
  44. Circle((0, 0, 0), A34, zAxis) → B34
  45. Circle((0, 0, 0), A35, zAxis) → B35
  46. Circle((0, 0, 0), A36, zAxis) → B36
  47. Circle((0, 0, 0), A37, zAxis) → B37
  48. Circle((0, 0, 0), A38, zAxis) → B38
  49. Circle((0, 0, 0), A39, zAxis) → B39
  50. Circle((0, 0, 0), A40, zAxis) → B40
  51. Circle((0, 0, 0), A41, zAxis) → B41
  52. Circle((0, 0, 0), A42, zAxis) → B42
  53. Circle((0, 0, 0), A43, zAxis) → B43
  54. Circle((0, 0, 0), A44, zAxis) → B44
  55. Circle((0, 0, 0), A45, zAxis) → B45
  56. Circle((0, 0, 0), A46, zAxis) → B46
  57. Circle((0, 0, 0), A47, zAxis) → B47
  58. Circle((0, 0, 0), A48, zAxis) → B48
  59. Circle((0, 0, 0), A49, zAxis) → B49
  60. Circle((0, 0, 0), A50, zAxis) → B50
  61. Circle((0, 0, 0), A51, zAxis) → B51
  62. Circle((0, 0, 0), A52, zAxis) → B52
  63. Circle((0, 0, 0), A53, zAxis) → B53
  64. Circle((0, 0, 0), A54, zAxis) → B54
  65. Circle((0, 0, 0), A55, zAxis) → B55
  66. Circle((0, 0, 0), A56, zAxis) → B56
  67. Circle((0, 0, 0), A57, zAxis) → B57
  68. Circle((0, 0, 0), A58, zAxis) → B58
  69. Circle((0, 0, 0), A59, zAxis) → B59
  70. Circle((0, 0, 0), A60, zAxis) → B60
  71. Circle((0, 0, 0), A61, zAxis) → B61
  72. Circle((0, 0, 0), A62, zAxis) → B62
  73. Circle((0, 0, 0), A63, zAxis) → B63
  74. Circle((0, 0, 0), A64, zAxis) → B64
  75. Circle((0, 0, 0), A65, zAxis) → B65
  76. Circle((0, 0, 0), A66, zAxis) → B66
  77. Circle((0, 0, 0), A67, zAxis) → B67
  78. Circle((0, 0, 0), A68, zAxis) → B68

AI Drawing Prompt Reference

Create a 3D sphere with a series of meridian-like curves on its surface, evenly spaced from bottom to top, each undulating in a wave-like pattern to create a luminous projection effect. A vertical axis passes through the sphere's center, with a point on it connected by a segment to a point on the sphere's surface, and another point on that segment. Outside the sphere, a set of concentric circles with radii slightly larger than the sphere, each carrying multiple small circles evenly spaced along their circumference, forming a dynamic spherical projection and geometric arrangement.
The prompt above was compiled from the original drawing commands and is for reference only.