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苹果2

苹果2
几何画板及绘图内容加载中，请稍等……
2020-01-17 05:24
函数三角函数微积分
这个范例演示了如何使用GeoGebra绘制苹果形状的曲面。涉及的核心数学概念包括曲面、微积分和三角函数。通过使用Surface、CurveCartesian、Sequence等命令，可以构造出复杂的几何图形。适合高中及以上学生学习和探索。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个苹果形状的曲面，包括两个对称的半球形表面和底部的凹陷部分。使用参数方程定义曲面，通过旋转和变换生成复杂的几何形状。首先绘制两个半球形表面，然后添加底部的凹陷部分，最后绘制苹果表面的细节，如斑点和凹痕。
以上提示语为根据原始绘图命令整理而来，仅供参考。