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Leaves in Nature (Surface Example)

Leaves in Nature (Surface Example)
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2020-09-25 05:03
TrigonometryCoordinate GeometryParametric Equation
This example demonstrates the surface morphology of leaves in nature. It involves core concepts of trigonometry and coordinate geometry. Using commands like CurveCartesian and Surface in GeoGebra, a 3D model of a leaf can be constructed. Suitable for high school and above students or teachers for teaching and learning.

GeoGebra Commands & Parameters

  1. Textfield(r) → ChampTexte1
  2. CurveCartesian(x(C) + (((sin(i) + sin((25 * i)) / 12) * R) * cos(i)), y(C) + (((sin(i) + sin((25 * i)) / 12) * R) * sin(i)), i, 0, 6.283185307179586) → c
  3. CurveCartesian(x(B) + (((sin(i) + sin((16 * i)) / 3) * R) * cos(i)), y(B) + (((sin(i) + sin((16 * i)) / 3) * R) * sin(i)), i, 0, 6.283185307179586) → b
  4. CurveCartesian(x(D) + (((sin(i) + sin((45 * i)) / 12) * R) * cos(i)), y(D) + (((sin(i) + sin((45 * i)) / 12) * R) * sin(i)), i, 0, 6.283185307179586) → d
  5. CurveCartesian(x(A) + ((r(i) * R) * cos(i)), y(A) + ((r(i) * R) * sin(i)), i, 0, t) → h
  6. Segment(E, H) → i
  7. Segment(C, M) → k
  8. Segment(G, I) → l
  9. Segment(F, J) → m
  10. Segment(B, K) → n
  11. Segment(D, L) → p
  12. CurveCartesian(x(F) + (((sin(i) + sin((55 * i / 15))) * R / 1.5) * cos(i)), y(F) + (((sin(i) + sin((55 * i / 15))) * R / 1.5) * sin(i)), i, 0, 18.84956) → f
  13. CurveCartesian(x(G) + (((sin(i) + sin((75 * i / 20))) * R / 1.5) * cos(i)), y(G) + (((sin(i) + sin((75 * i / 20))) * R / 1.5) * sin(i)), i, 0, 15.707963267948966) → g
  14. CurveCartesian(x(E) + (((sin(i) + sin((25 * i / 4))) * R / 2) * cos(i)), y(E) + (((sin(i) + sin((25 * i / 4))) * R / 2) * sin(i)), z(E), i, 0, 6.28319) → e
  15. CurveCartesian(x(E) + (0.1 * cos(i)), y(E) + (0.1 * sin(i)), z(E), i, 0, (2 * π)) → o
  16. Surface((b * e(a)) + ((1 - b) * o(a)), a, 0, (2 * π), b, 0, 1) → q
  17. CurveCartesian(x(C) + (0.1 * cos(i)), y(C) + (0.1 * sin(i)), z(C), i, 0, (2 * π)) → s
  18. Surface((b * c(a)) + ((1 - b) * s(a)), a, 0, (2 * π), b, 0, 1) → u
  19. CurveCartesian(x(G) + (0.1 * cos(i)), y(G) + (0.1 * sin(i)), z(G), i, 0, (2 * π)) → v
  20. Surface((b * g(a)) + ((1 - b) * v(a)), a, 0, (5 * π), b, 0, 1) → w
  21. CurveCartesian(x(F) + (0.1 * cos(i)), y(F) + (0.1 * sin(i)), z(F), i, 0, (2 * π)) → a_1
  22. Surface((b * f(a)) + ((1 - b) * a_1(a)), a, 0, (5 * π), b, 0, 1) → b_1
  23. CurveCartesian(x(D) + (0.1 * cos(i)), y(D) + (0.1 * sin(i)), z(D), i, 0, (2 * π)) → c_1
  24. Surface((b * d(a)) + ((1 - b) * c_1(a)), a, 0, (5 * π), b, 0, 1) → d_1
  25. CurveCartesian(x(B) + (0.1 * cos(i)), y(B) + (0.1 * sin(i)), z(B), i, 0, (2 * π)) → e_1
  26. Surface((b * b(a)) + ((1 - b) * e_1(a)), a, 0, (5 * π), b, 0, 1) → f_1
  27. CurveCartesian(x(A) + (0.1 * cos(i)), y(A) + (0.1 * sin(i)), z(A), i, 0, (2 * π)) → g_1
  28. CurveCartesian(x(A) + ((r(i) * R / 1.25) * cos(i)), y(A) + ((r(i) * R / 1.25) * sin(i)), i, 0, t) → a
  29. Surface((b * a(a)) + ((1 - b) * g_1(a)), a, 0, (5 * π), b, 0, 1) → h_1
  30. Segment(A, N) → i_1

AI Drawing Prompt Reference

Draw the surface morphology of leaves in nature to showcase their 3D structure. Use sinusoidal functions and parametric equations to generate the outlines of the leaves, combining curves with different parameters to form the立体 effect of the leaves. Start by drawing the basic outlines, add detailed curves, and finally combine the curves with planes to generate 3D surfaces, presenting a realistic leaf shape.
The prompt above was compiled from the original drawing commands and is for reference only.