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3D Fourier Transform Visualization by Patrick Clément

3D Fourier Transform Visualization by Patrick Clément
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2014-10-25 21:08
FunctionTrigonometrySolid Geometry
In collections surface 3D surface 3D My 3D Collection
This example visualizes 3D Fourier transforms. It involves Fourier series and 3D geometry. Using commands like PointIn, Sequence, Surface, and CurveCartesian, complex 3D shapes can be constructed. Suitable for university mathematics and related researchers and learners.

GeoGebra Commands & Parameters

  1. PointIn(x + (0 * z) = 1) → B
  2. PointIn(x + (0 * z) = 2) → C
  3. PointIn(x + (0 * z) = 3) → D
  4. PointIn(x + (0 * z) = 4) → E
  5. PointIn(x + (0 * z) = 7) → H
  6. PointIn(x + (0 * z) = 8) → I
  7. PointIn(x + (0 * z) = 9) → J
  8. PointIn(x + (0 * z) = 10) → K
  9. PointIn(x + (0 * z) = 11) → L
  10. PointIn(x + (0 * z) = 5) → F
  11. PointIn(x + (0 * z) = 0) → A
  12. Sequence((k + 6, ((-1)^(k + 1) * 2 / k)), k, 1, 5) → dent
  13. Sequence((k, (2 / ((π * k^(2))) * (cos((k * π)) - 1))), k, 1, 5) → tri
  14. Sequence((i, (6 / ((i * π)) * sin((i * π / 2)))), i, 1, 5) → cren
  15. Surface((u * cos(v)), (u * sin(v)), f(u), u, 0, (eu * T), v, 0, ev) → s
  16. CurveCartesian(t, 0, f(t), t, 0, (eu * T)) → d
  17. CurveCartesian(t, f(t), t, 0, (eu * T)) → c

AI Drawing Prompt Reference

Create a 3D visualization of a Fourier transform. First, create 10 points on the x-axis with coordinates 1, 2, 3, 4, 5, 7, 8, 9, 10, and 11, and one point at 0. Then, draw a series of triangular, sawtooth, and cosine curves, which will serve as the basis for the 3D surface. Finally, use these curves and points to create a 3D surface and two 3D curves.
The prompt above was compiled from the original drawing commands and is for reference only.