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Apple Surface

Apple Surface
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2020-01-17 05:24
FunctionTrigonometryCalculus
This example demonstrates how to draw an apple-shaped surface using GeoGebra. Key mathematical concepts include surface, calculus, and trigonometric functions. By using commands like Surface, CurveCartesian, and Sequence, complex geometric shapes can be constructed. Suitable for high school and above students to learn and explore.

GeoGebra Commands & Parameters

  1. Surface(x(B) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(B) + ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(B) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 0, 3.141592653589793, v, -2.20159, 2.6415) → b
  2. Surface(x(B) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(B) + ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(B) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 0, 3.141592653589793, v, 2.6415, 3.141592653589793) → c
  3. Surface(x(A) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(A) - ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 0, 3.141592653589793, v, -2.20159, 2.6415) → f
  4. CurveCartesian(x(A) + (R * (4 + (3.8 * cos(v)))), y(A), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), v, -2.20159, 2.6415) → e
  5. CurveCartesian(x(A) - (R * (4 + (3.8 * cos(v)))), y(A), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), v, -2.20159, 2.6415) → g
  6. Sequence((x(A) - (R * (4 + (3.8 * cos(v)))), y(A), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v))))), v, -3.14159, 4.71239, 0.2) → liste1
  7. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], A], i, 1, Length[liste1]) → liste2
  8. Sequence((x(A) + (R * (4 + (3.8 * cos(v)))), y(A), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v))))), v, -3.14159, 4.71239, 0.2) → liste3
  9. Sequence(Polygon[Element[liste3, i], Element[liste3, i + 1], A], i, 1, Length[liste3]) → liste4
  10. Sequence((x(B) - (R * (4 + (3.8 * cos(v)))), y(B), z(B) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v))))), v, -3.14159, 4.71238898038469, 0.2) → liste5
  11. Sequence((x(B) + (R * (4 + (3.8 * cos(v)))), y(B), z(B) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v))))), v, -3.14159, 4.71238898038469, 0.2) → liste6
  12. Sequence(Polygon[Element[liste6, i], Element[liste6, i + 1], B], i, 1, Length[liste6]) → liste8
  13. Sequence(Polygon[Element[liste5, i], Element[liste5, i + 1], B], i, 1, Length[liste5]) → liste7
  14. Surface(x(A) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(A) - ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 0, 3.141592653589793, v, 2.6415, 3.141592653589793) → h
  15. Surface(x(B) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(B) + ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(B) + 0.2 - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 0, 3.141592653589793, v, -3.14159, -2.2) → d
  16. Polygon(C, D, A) → poly1, a_1, c_1, d_1
  17. Polygon(E, F, B) → poly2, b_1, e_1, f_1
  18. Polygon(A, G, H) → poly3, h_1, a_2, g_1
  19. Polygon(B, K, J) → poly4, j_1, b_2, k
  20. Surface(x(A) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(A) - ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(A) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 0, 3.141592653589793, v, -3.14159, -2.2) → i
  21. Surface(x(B) + ((R * cos(u)) * (4 + (3.8 * cos(v)))), y(B) - ((R * sin(u)) * (4 + (3.8 * cos(v)))), z(B) - (R * ((((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (7.5 * sin(v)))), u, 3.141592653589793, 6.28319, v, -3.14159, -2.22) → l
  22. CurveCartesian(x(A) + (2.5 * cos(t)), y(A), z(A) + (2 * sin(t)), t, 0, 6.28319) → j
  23. CurveCartesian(x(L) + (0.15 * cos(t)), y(L) - 0.3, z(L) + (0.3 * sin(t)), t, 0, 6.28319) → m
  24. CurveCartesian(x(M) + (0.15 * cos(t)), y(M) - 0.3, z(M) + (0.3 * sin(t)), t, 0, 6.28319) → n
  25. CurveCartesian(x(N) + (0.15 * cos(t)), y(N) - 0.3, z(N) + (0.3 * sin(t)), t, 0, 6.28319) → o
  26. CurveCartesian(x(P) + (0.15 * cos(t)), y(P) - 0.3, z(P) + (0.3 * sin(t)), t, 0, 6.28319) → p
  27. CircumcircleArc(C, Q, A) → q
  28. CircumcircleArc(D, S, A) → r
  29. PointIn(poly2) → V
  30. CircumcircleArc(F, U, B) → s
  31. PointIn(poly2) → W
  32. CircumcircleArc(E, T, V) → t
  33. Point(liste2) → C_1
  34. CircumcircleArc(A_1, Z, B_1) → k_1
  35. Mirror(k_1, A) → p_1
  36. Mirror(k_1, O) → q_1
  37. Mirror(p_1, O) → r_1
  38. CircumcircleArc(E_1, D_1, A) → s_1
  39. CircumcircleArc(F_1, G_1, A) → t_1
  40. Line(O, H_1) → i_1
  41. Mirror(t_1, i_1) → c_2
  42. Mirror(s_1, i_1) → d_2

AI Drawing Prompt Reference

Draw an apple-shaped surface with two symmetric hemispherical surfaces and a bottom indentation. Use parametric equations to define the surface and generate complex geometric shapes through rotation and transformation. First, draw the two hemispherical surfaces, then add the bottom indentation, and finally, draw the details of the apple surface, such as spots and indentations.
The prompt above was compiled from the original drawing commands and is for reference only.