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三维函数集合：曲面层叠

三维函数集合：曲面层叠
几何画板及绘图内容加载中，请稍等……
2013-11-12 21:22
函数解析几何参数方程函数图像
所属专题 surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
该范例展示了34个预定义的三维函数z=f(x,y)，通过层叠曲线来构建曲面。核心数学概念包括函数、参数方程和解析几何。使用了Element、Function、CurveCartesian等GeoGebra命令。适合高中及以上学生学习三维几何和函数图像。

GeoGebra 命令及参数

  1. Element(lFr, Funktion) → fxx
  2. Textfield(x0_{min}) → inputBox1
  3. Textfield(x0_{max}) → inputBox2
  4. Textfield(y0_{min}) → inputBox3
  5. Textfield(y0_{max}) → inputBox4
  6. Textfield(g00r) → inputBox5
  7. Textfield(Funktion) → Textfeld1
  8. Function(fxx(a, b), a, x0_{min}, x0_{max}, b, y0_{min}, y0_{max}) → f0
  9. Element(l, Funktion) → Text4
  10. Element(l, Funktion) → Tinfo1
  11. CurveCartesian(t, -3.2, fxx(t, (-3.2)), t, x0_{min}, x0_{max}) → M4_{1}
  12. CurveCartesian(-3.2, t, fxx((-3.2), t), t, y0_{min}, y0_{max}) → M5_{1}
  13. CurveCartesian(t, -3.072, fxx(t, (-3.072)), t, x0_{min}, x0_{max}) → M4_{2}
  14. CurveCartesian(-3.072, t, fxx((-3.072), t), t, y0_{min}, y0_{max}) → M5_{2}
  15. CurveCartesian(t, -2.944, fxx(t, (-2.944)), t, x0_{min}, x0_{max}) → M4_{3}
  16. CurveCartesian(-2.944, t, fxx((-2.944), t), t, y0_{min}, y0_{max}) → M5_{3}
  17. CurveCartesian(t, -2.8160000000000003, fxx(t, (-2.8160000000000003)), t, x0_{min}, x0_{max}) → M4_{4}
  18. CurveCartesian(-2.8160000000000003, t, fxx((-2.8160000000000003), t), t, y0_{min}, y0_{max}) → M5_{4}
  19. CurveCartesian(t, -2.688, fxx(t, (-2.688)), t, x0_{min}, x0_{max}) → M4_{5}
  20. CurveCartesian(-2.688, t, fxx((-2.688), t), t, y0_{min}, y0_{max}) → M5_{5}
  21. CurveCartesian(t, -2.56, fxx(t, (-2.56)), t, x0_{min}, x0_{max}) → M4_{6}
  22. CurveCartesian(-2.56, t, fxx((-2.56), t), t, y0_{min}, y0_{max}) → M5_{6}
  23. CurveCartesian(t, -2.4320000000000004, fxx(t, (-2.4320000000000004)), t, x0_{min}, x0_{max}) → M4_{7}
  24. CurveCartesian(-2.4320000000000004, t, fxx((-2.4320000000000004), t), t, y0_{min}, y0_{max}) → M5_{7}
  25. CurveCartesian(t, -2.3040000000000003, fxx(t, (-2.3040000000000003)), t, x0_{min}, x0_{max}) → M4_{8}
  26. CurveCartesian(-2.3040000000000003, t, fxx((-2.3040000000000003), t), t, y0_{min}, y0_{max}) → M5_{8}
  27. CurveCartesian(t, -2.176, fxx(t, (-2.176)), t, x0_{min}, x0_{max}) → M4_{9}
  28. CurveCartesian(-2.176, t, fxx((-2.176), t), t, y0_{min}, y0_{max}) → M5_{9}
  29. CurveCartesian(t, -2.048, fxx(t, (-2.048)), t, x0_{min}, x0_{max}) → M4_{10}
  30. CurveCartesian(-2.048, t, fxx((-2.048), t), t, y0_{min}, y0_{max}) → M5_{10}
  31. CurveCartesian(t, -1.9200000000000002, fxx(t, (-1.9200000000000002)), t, x0_{min}, x0_{max}) → M4_{11}
  32. CurveCartesian(-1.9200000000000002, t, fxx((-1.9200000000000002), t), t, y0_{min}, y0_{max}) → M5_{11}
  33. CurveCartesian(t, -1.7920000000000003, fxx(t, (-1.7920000000000003)), t, x0_{min}, x0_{max}) → M4_{12}
  34. CurveCartesian(-1.7920000000000003, t, fxx((-1.7920000000000003), t), t, y0_{min}, y0_{max}) → M5_{12}
  35. CurveCartesian(t, -1.6640000000000001, fxx(t, (-1.6640000000000001)), t, x0_{min}, x0_{max}) → M4_{13}
  36. CurveCartesian(-1.6640000000000001, t, fxx((-1.6640000000000001), t), t, y0_{min}, y0_{max}) → M5_{13}
  37. CurveCartesian(t, -1.536, fxx(t, (-1.536)), t, x0_{min}, x0_{max}) → M4_{14}
  38. CurveCartesian(-1.536, t, fxx((-1.536), t), t, y0_{min}, y0_{max}) → M5_{14}
  39. CurveCartesian(t, -1.4080000000000001, fxx(t, (-1.4080000000000001)), t, x0_{min}, x0_{max}) → M4_{15}
  40. CurveCartesian(-1.4080000000000001, t, fxx((-1.4080000000000001), t), t, y0_{min}, y0_{max}) → M5_{15}
  41. CurveCartesian(t, -1.2800000000000002, fxx(t, (-1.2800000000000002)), t, x0_{min}, x0_{max}) → M4_{16}
  42. CurveCartesian(-1.2800000000000002, t, fxx((-1.2800000000000002), t), t, y0_{min}, y0_{max}) → M5_{16}
  43. CurveCartesian(t, -1.1520000000000001, fxx(t, (-1.1520000000000001)), t, x0_{min}, x0_{max}) → M4_{17}
  44. CurveCartesian(-1.1520000000000001, t, fxx((-1.1520000000000001), t), t, y0_{min}, y0_{max}) → M5_{17}
  45. CurveCartesian(t, -1.024, fxx(t, (-1.024)), t, x0_{min}, x0_{max}) → M4_{18}
  46. CurveCartesian(-1.024, t, fxx((-1.024), t), t, y0_{min}, y0_{max}) → M5_{18}
  47. CurveCartesian(t, -0.8959999999999999, fxx(t, (-0.8959999999999999)), t, x0_{min}, x0_{max}) → M4_{19}
  48. CurveCartesian(-0.8959999999999999, t, fxx((-0.8959999999999999), t), t, y0_{min}, y0_{max}) → M5_{19}
  49. CurveCartesian(t, -0.7680000000000002, fxx(t, (-0.7680000000000002)), t, x0_{min}, x0_{max}) → M4_{20}
  50. CurveCartesian(-0.7680000000000002, t, fxx((-0.7680000000000002), t), t, y0_{min}, y0_{max}) → M5_{20}
  51. CurveCartesian(t, -0.6400000000000001, fxx(t, (-0.6400000000000001)), t, x0_{min}, x0_{max}) → M4_{21}
  52. CurveCartesian(-0.6400000000000001, t, fxx((-0.6400000000000001), t), t, y0_{min}, y0_{max}) → M5_{21}
  53. CurveCartesian(t, -0.512, fxx(t, (-0.512)), t, x0_{min}, x0_{max}) → M4_{22}
  54. CurveCartesian(-0.512, t, fxx((-0.512), t), t, y0_{min}, y0_{max}) → M5_{22}
  55. CurveCartesian(t, -0.38400000000000034, fxx(t, (-0.38400000000000034)), t, x0_{min}, x0_{max}) → M4_{23}
  56. CurveCartesian(-0.38400000000000034, t, fxx((-0.38400000000000034), t), t, y0_{min}, y0_{max}) → M5_{23}
  57. CurveCartesian(t, -0.2560000000000002, fxx(t, (-0.2560000000000002)), t, x0_{min}, x0_{max}) → M4_{24}
  58. CurveCartesian(-0.2560000000000002, t, fxx((-0.2560000000000002), t), t, y0_{min}, y0_{max}) → M5_{24}
  59. CurveCartesian(t, -0.1280000000000001, fxx(t, (-0.1280000000000001)), t, x0_{min}, x0_{max}) → M4_{25}
  60. CurveCartesian(-0.1280000000000001, t, fxx((-0.1280000000000001), t), t, y0_{min}, y0_{max}) → M5_{25}
  61. CurveCartesian(t, 0, fxx(t, 0), t, x0_{min}, x0_{max}) → M4_{26}
  62. CurveCartesian(0, t, fxx(0, t), t, y0_{min}, y0_{max}) → M5_{26}
  63. CurveCartesian(t, 0.1280000000000001, fxx(t, 0.1280000000000001), t, x0_{min}, x0_{max}) → M4_{27}
  64. CurveCartesian(0.1280000000000001, t, fxx(0.1280000000000001, t), t, y0_{min}, y0_{max}) → M5_{27}
  65. CurveCartesian(t, 0.2559999999999998, fxx(t, 0.2559999999999998), t, x0_{min}, x0_{max}) → M4_{28}
  66. CurveCartesian(0.2559999999999998, t, fxx(0.2559999999999998, t), t, y0_{min}, y0_{max}) → M5_{28}
  67. CurveCartesian(t, 0.3839999999999999, fxx(t, 0.3839999999999999), t, x0_{min}, x0_{max}) → M4_{29}
  68. CurveCartesian(0.3839999999999999, t, fxx(0.3839999999999999, t), t, y0_{min}, y0_{max}) → M5_{29}
  69. CurveCartesian(t, 0.512, fxx(t, 0.512), t, x0_{min}, x0_{max}) → M4_{30}
  70. CurveCartesian(0.512, t, fxx(0.512, t), t, y0_{min}, y0_{max}) → M5_{30}
  71. CurveCartesian(t, 0.6399999999999997, fxx(t, 0.6399999999999997), t, x0_{min}, x0_{max}) → M4_{31}
  72. CurveCartesian(0.6399999999999997, t, fxx(0.6399999999999997, t), t, y0_{min}, y0_{max}) → M5_{31}
  73. CurveCartesian(t, 0.7679999999999998, fxx(t, 0.7679999999999998), t, x0_{min}, x0_{max}) → M4_{32}
  74. CurveCartesian(0.7679999999999998, t, fxx(0.7679999999999998, t), t, y0_{min}, y0_{max}) → M5_{32}
  75. CurveCartesian(t, 0.8959999999999999, fxx(t, 0.8959999999999999), t, x0_{min}, x0_{max}) → M4_{33}
  76. CurveCartesian(0.8959999999999999, t, fxx(0.8959999999999999, t), t, y0_{min}, y0_{max}) → M5_{33}
  77. CurveCartesian(t, 1.024, fxx(t, 1.024), t, x0_{min}, x0_{max}) → M4_{34}
  78. CurveCartesian(1.024, t, fxx(1.024, t), t, y0_{min}, y0_{max}) → M5_{34}
  79. CurveCartesian(t, 1.1520000000000001, fxx(t, 1.1520000000000001), t, x0_{min}, x0_{max}) → M4_{35}
  80. CurveCartesian(1.1520000000000001, t, fxx(1.1520000000000001, t), t, y0_{min}, y0_{max}) → M5_{35}
  81. CurveCartesian(t, 1.2800000000000002, fxx(t, 1.2800000000000002), t, x0_{min}, x0_{max}) → M4_{36}
  82. CurveCartesian(1.2800000000000002, t, fxx(1.2800000000000002, t), t, y0_{min}, y0_{max}) → M5_{36}
  83. CurveCartesian(t, 1.4080000000000004, fxx(t, 1.4080000000000004), t, x0_{min}, x0_{max}) → M4_{37}
  84. CurveCartesian(1.4080000000000004, t, fxx(1.4080000000000004, t), t, y0_{min}, y0_{max}) → M5_{37}
  85. CurveCartesian(t, 1.5359999999999996, fxx(t, 1.5359999999999996), t, x0_{min}, x0_{max}) → M4_{38}
  86. CurveCartesian(1.5359999999999996, t, fxx(1.5359999999999996, t), t, y0_{min}, y0_{max}) → M5_{38}
  87. CurveCartesian(t, 1.6639999999999997, fxx(t, 1.6639999999999997), t, x0_{min}, x0_{max}) → M4_{39}
  88. CurveCartesian(1.6639999999999997, t, fxx(1.6639999999999997, t), t, y0_{min}, y0_{max}) → M5_{39}
  89. CurveCartesian(t, 1.7919999999999998, fxx(t, 1.7919999999999998), t, x0_{min}, x0_{max}) → M4_{40}
  90. CurveCartesian(1.7919999999999998, t, fxx(1.7919999999999998, t), t, y0_{min}, y0_{max}) → M5_{40}
  91. CurveCartesian(t, 1.92, fxx(t, 1.92), t, x0_{min}, x0_{max}) → M4_{41}
  92. CurveCartesian(1.92, t, fxx(1.92, t), t, y0_{min}, y0_{max}) → M5_{41}
  93. CurveCartesian(t, 2.048, fxx(t, 2.048), t, x0_{min}, x0_{max}) → M4_{42}
  94. CurveCartesian(2.048, t, fxx(2.048, t), t, y0_{min}, y0_{max}) → M5_{42}
  95. CurveCartesian(t, 2.176, fxx(t, 2.176), t, x0_{min}, x0_{max}) → M4_{43}
  96. CurveCartesian(2.176, t, fxx(2.176, t), t, y0_{min}, y0_{max}) → M5_{43}
  97. CurveCartesian(t, 2.3040000000000003, fxx(t, 2.3040000000000003), t, x0_{min}, x0_{max}) → M4_{44}
  98. CurveCartesian(2.3040000000000003, t, fxx(2.3040000000000003, t), t, y0_{min}, y0_{max}) → M5_{44}
  99. CurveCartesian(t, 2.4319999999999995, fxx(t, 2.4319999999999995), t, x0_{min}, x0_{max}) → M4_{45}
  100. CurveCartesian(2.4319999999999995, t, fxx(2.4319999999999995, t), t, y0_{min}, y0_{max}) → M5_{45}
  101. CurveCartesian(t, 2.5599999999999996, fxx(t, 2.5599999999999996), t, x0_{min}, x0_{max}) → M4_{46}
  102. CurveCartesian(2.5599999999999996, t, fxx(2.5599999999999996, t), t, y0_{min}, y0_{max}) → M5_{46}
  103. CurveCartesian(t, 2.6879999999999997, fxx(t, 2.6879999999999997), t, x0_{min}, x0_{max}) → M4_{47}
  104. CurveCartesian(2.6879999999999997, t, fxx(2.6879999999999997, t), t, y0_{min}, y0_{max}) → M5_{47}
  105. CurveCartesian(t, 2.816, fxx(t, 2.816), t, x0_{min}, x0_{max}) → M4_{48}
  106. CurveCartesian(2.816, t, fxx(2.816, t), t, y0_{min}, y0_{max}) → M5_{48}
  107. CurveCartesian(t, 2.944, fxx(t, 2.944), t, x0_{min}, x0_{max}) → M4_{49}
  108. CurveCartesian(2.944, t, fxx(2.944, t), t, y0_{min}, y0_{max}) → M5_{49}
  109. CurveCartesian(t, 3.072, fxx(t, 3.072), t, x0_{min}, x0_{max}) → M4_{50}
  110. CurveCartesian(3.072, t, fxx(3.072, t), t, y0_{min}, y0_{max}) → M5_{50}
  111. CurveCartesian(t, 3.2, fxx(t, 3.2), t, x0_{min}, x0_{max}) → M4_{51}
  112. CurveCartesian(3.2, t, fxx(3.2, t), t, y0_{min}, y0_{max}) → M5_{51}

AI 绘图提示语参考

绘制一个三维函数集合，展示34个预定义的三维函数z=f(x,y)。通过层叠曲线构建曲面，使用输入框设置x和y的最小最大值，以及函数表达式。首先设置x和y的范围，然后输入函数表达式，最后根据给定的t值绘制一系列曲线，形成曲面层叠效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。