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罗马曲面网格效果

罗马曲面网格效果
几何画板及绘图内容加载中，请稍等……
2014-06-05 18:45
函数解析几何立体几何
所属专题 surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
这是一个展示罗马曲面网格效果的GeoGebra 3D范例。罗马曲面是一种特殊的四次曲面，具有独特的几何形态。通过使用曲面曲线，可以构建出精美的网格效果。本范例使用了Surface、CurveCartesian等GeoGebra命令，通过调整参数可以观察到曲面的变化。适合高中数学教学和学习立体几何的学生。

GeoGebra 命令及参数

  1. Textfield(NN) → inputBox5
  2. Textfield(fx) → inputBox1
  3. Textfield(fy) → inputBox2
  4. Textfield(fz) → inputBox3
  5. Textfield(u_{min}) → inputBox4
  6. Textfield(u_{max}) → inputBox6
  7. Textfield(v_{min}) → inputBox7
  8. Textfield(v_{max}) → inputBox8
  9. Surface((Zoom * fx(u, v)), (Zoom * fy(u, v)), (Zoom * fz(u, v)), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → f3
  10. CurveCartesian((Zoom * fx(t, (-1.57))), (Zoom * fy(t, (-1.57))), (Zoom * fz(t, (-1.57))), t, u_{min}, u_{max}) → M4_{1}
  11. CurveCartesian((Zoom * fx((-1.57), t)), (Zoom * fy((-1.57), t)), (Zoom * fz((-1.57), t)), t, v_{min}, v_{max}) → M5_{1}
  12. CurveCartesian((Zoom * fx(t, (-1.5071840734641022))), (Zoom * fy(t, (-1.5071840734641022))), (Zoom * fz(t, (-1.5071840734641022))), t, u_{min}, u_{max}) → M4_{2}
  13. CurveCartesian((Zoom * fx((-1.5072), t)), (Zoom * fy((-1.5072), t)), (Zoom * fz((-1.5072), t)), t, v_{min}, v_{max}) → M5_{2}
  14. CurveCartesian((Zoom * fx(t, (-1.4443681469282041))), (Zoom * fy(t, (-1.4443681469282041))), (Zoom * fz(t, (-1.4443681469282041))), t, u_{min}, u_{max}) → M4_{3}
  15. CurveCartesian((Zoom * fx((-1.4444000000000001), t)), (Zoom * fy((-1.4444000000000001), t)), (Zoom * fz((-1.4444000000000001), t)), t, v_{min}, v_{max}) → M5_{3}
  16. CurveCartesian((Zoom * fx(t, (-1.3815522203923063))), (Zoom * fy(t, (-1.3815522203923063))), (Zoom * fz(t, (-1.3815522203923063))), t, u_{min}, u_{max}) → M4_{4}
  17. CurveCartesian((Zoom * fx((-1.3816000000000002), t)), (Zoom * fy((-1.3816000000000002), t)), (Zoom * fz((-1.3816000000000002), t)), t, v_{min}, v_{max}) → M5_{4}
  18. CurveCartesian((Zoom * fx(t, (-1.3187362938564084))), (Zoom * fy(t, (-1.3187362938564084))), (Zoom * fz(t, (-1.3187362938564084))), t, u_{min}, u_{max}) → M4_{5}
  19. CurveCartesian((Zoom * fx((-1.3188), t)), (Zoom * fy((-1.3188), t)), (Zoom * fz((-1.3188), t)), t, v_{min}, v_{max}) → M5_{5}
  20. CurveCartesian((Zoom * fx(t, (-1.2559203673205104))), (Zoom * fy(t, (-1.2559203673205104))), (Zoom * fz(t, (-1.2559203673205104))), t, u_{min}, u_{max}) → M4_{6}
  21. CurveCartesian((Zoom * fx((-1.256), t)), (Zoom * fy((-1.256), t)), (Zoom * fz((-1.256), t)), t, v_{min}, v_{max}) → M5_{6}
  22. CurveCartesian((Zoom * fx(t, (-1.1931044407846125))), (Zoom * fy(t, (-1.1931044407846125))), (Zoom * fz(t, (-1.1931044407846125))), t, u_{min}, u_{max}) → M4_{7}
  23. CurveCartesian((Zoom * fx((-1.1932), t)), (Zoom * fy((-1.1932), t)), (Zoom * fz((-1.1932), t)), t, v_{min}, v_{max}) → M5_{7}
  24. CurveCartesian((Zoom * fx(t, (-1.1302885142487145))), (Zoom * fy(t, (-1.1302885142487145))), (Zoom * fz(t, (-1.1302885142487145))), t, u_{min}, u_{max}) → M4_{8}
  25. CurveCartesian((Zoom * fx((-1.1304), t)), (Zoom * fy((-1.1304), t)), (Zoom * fz((-1.1304), t)), t, v_{min}, v_{max}) → M5_{8}
  26. CurveCartesian((Zoom * fx(t, (-1.0674725877128166))), (Zoom * fy(t, (-1.0674725877128166))), (Zoom * fz(t, (-1.0674725877128166))), t, u_{min}, u_{max}) → M4_{9}
  27. CurveCartesian((Zoom * fx((-1.0676), t)), (Zoom * fy((-1.0676), t)), (Zoom * fz((-1.0676), t)), t, v_{min}, v_{max}) → M5_{9}
  28. CurveCartesian((Zoom * fx(t, (-1.0046566611769188))), (Zoom * fy(t, (-1.0046566611769188))), (Zoom * fz(t, (-1.0046566611769188))), t, u_{min}, u_{max}) → M4_{10}
  29. CurveCartesian((Zoom * fx((-1.0048), t)), (Zoom * fy((-1.0048), t)), (Zoom * fz((-1.0048), t)), t, v_{min}, v_{max}) → M5_{10}
  30. CurveCartesian((Zoom * fx(t, (-0.9418407346410207))), (Zoom * fy(t, (-0.9418407346410207))), (Zoom * fz(t, (-0.9418407346410207))), t, u_{min}, u_{max}) → M4_{11}
  31. CurveCartesian((Zoom * fx((-0.942), t)), (Zoom * fy((-0.942), t)), (Zoom * fz((-0.942), t)), t, v_{min}, v_{max}) → M5_{11}
  32. CurveCartesian((Zoom * fx(t, (-0.8790248081051228))), (Zoom * fy(t, (-0.8790248081051228))), (Zoom * fz(t, (-0.8790248081051228))), t, u_{min}, u_{max}) → M4_{12}
  33. CurveCartesian((Zoom * fx((-0.8792), t)), (Zoom * fy((-0.8792), t)), (Zoom * fz((-0.8792), t)), t, v_{min}, v_{max}) → M5_{12}
  34. CurveCartesian((Zoom * fx(t, (-0.8162088815692249))), (Zoom * fy(t, (-0.8162088815692249))), (Zoom * fz(t, (-0.8162088815692249))), t, u_{min}, u_{max}) → M4_{13}
  35. CurveCartesian((Zoom * fx((-0.8164), t)), (Zoom * fy((-0.8164), t)), (Zoom * fz((-0.8164), t)), t, v_{min}, v_{max}) → M5_{13}
  36. CurveCartesian((Zoom * fx(t, (-0.7533929550333269))), (Zoom * fy(t, (-0.7533929550333269))), (Zoom * fz(t, (-0.7533929550333269))), t, u_{min}, u_{max}) → M4_{14}
  37. CurveCartesian((Zoom * fx((-0.7535999999999999), t)), (Zoom * fy((-0.7535999999999999), t)), (Zoom * fz((-0.7535999999999999), t)), t, v_{min}, v_{max}) → M5_{14}
  38. CurveCartesian((Zoom * fx(t, (-0.6905770284974291))), (Zoom * fy(t, (-0.6905770284974291))), (Zoom * fz(t, (-0.6905770284974291))), t, u_{min}, u_{max}) → M4_{15}
  39. CurveCartesian((Zoom * fx((-0.6908), t)), (Zoom * fy((-0.6908), t)), (Zoom * fz((-0.6908), t)), t, v_{min}, v_{max}) → M5_{15}
  40. CurveCartesian((Zoom * fx(t, (-0.6277611019615311))), (Zoom * fy(t, (-0.6277611019615311))), (Zoom * fz(t, (-0.6277611019615311))), t, u_{min}, u_{max}) → M4_{16}
  41. CurveCartesian((Zoom * fx((-0.6279999999999999), t)), (Zoom * fy((-0.6279999999999999), t)), (Zoom * fz((-0.6279999999999999), t)), t, v_{min}, v_{max}) → M5_{16}
  42. CurveCartesian((Zoom * fx(t, (-0.5649451754256332))), (Zoom * fy(t, (-0.5649451754256332))), (Zoom * fz(t, (-0.5649451754256332))), t, u_{min}, u_{max}) → M4_{17}
  43. CurveCartesian((Zoom * fx((-0.5651999999999999), t)), (Zoom * fy((-0.5651999999999999), t)), (Zoom * fz((-0.5651999999999999), t)), t, v_{min}, v_{max}) → M5_{17}
  44. CurveCartesian((Zoom * fx(t, (-0.5021292488897353))), (Zoom * fy(t, (-0.5021292488897353))), (Zoom * fz(t, (-0.5021292488897353))), t, u_{min}, u_{max}) → M4_{18}
  45. CurveCartesian((Zoom * fx((-0.5024), t)), (Zoom * fy((-0.5024), t)), (Zoom * fz((-0.5024), t)), t, v_{min}, v_{max}) → M5_{18}
  46. CurveCartesian((Zoom * fx(t, (-0.43931332235383724))), (Zoom * fy(t, (-0.43931332235383724))), (Zoom * fz(t, (-0.43931332235383724))), t, u_{min}, u_{max}) → M4_{19}
  47. CurveCartesian((Zoom * fx((-0.4396), t)), (Zoom * fy((-0.4396), t)), (Zoom * fz((-0.4396), t)), t, v_{min}, v_{max}) → M5_{19}
  48. CurveCartesian((Zoom * fx(t, (-0.3764973958179394))), (Zoom * fy(t, (-0.3764973958179394))), (Zoom * fz(t, (-0.3764973958179394))), t, u_{min}, u_{max}) → M4_{20}
  49. CurveCartesian((Zoom * fx((-0.3767999999999998), t)), (Zoom * fy((-0.3767999999999998), t)), (Zoom * fz((-0.3767999999999998), t)), t, v_{min}, v_{max}) → M5_{20}
  50. CurveCartesian((Zoom * fx(t, (-0.3136814692820413))), (Zoom * fy(t, (-0.3136814692820413))), (Zoom * fz(t, (-0.3136814692820413))), t, u_{min}, u_{max}) → M4_{21}
  51. CurveCartesian((Zoom * fx((-0.31399999999999983), t)), (Zoom * fy((-0.31399999999999983), t)), (Zoom * fz((-0.31399999999999983), t)), t, v_{min}, v_{max}) → M5_{21}
  52. CurveCartesian((Zoom * fx(t, (-0.2508655427461435))), (Zoom * fy(t, (-0.2508655427461435))), (Zoom * fz(t, (-0.2508655427461435))), t, u_{min}, u_{max}) → M4_{22}
  53. CurveCartesian((Zoom * fx((-0.25119999999999987), t)), (Zoom * fy((-0.25119999999999987), t)), (Zoom * fz((-0.25119999999999987), t)), t, v_{min}, v_{max}) → M5_{22}
  54. CurveCartesian((Zoom * fx(t, (-0.18804961621024563))), (Zoom * fy(t, (-0.18804961621024563))), (Zoom * fz(t, (-0.18804961621024563))), t, u_{min}, u_{max}) → M4_{23}
  55. CurveCartesian((Zoom * fx((-0.1883999999999999), t)), (Zoom * fy((-0.1883999999999999), t)), (Zoom * fz((-0.1883999999999999), t)), t, v_{min}, v_{max}) → M5_{23}
  56. CurveCartesian((Zoom * fx(t, (-0.12523368967434756))), (Zoom * fy(t, (-0.12523368967434756))), (Zoom * fz(t, (-0.12523368967434756))), t, u_{min}, u_{max}) → M4_{24}
  57. CurveCartesian((Zoom * fx((-0.12559999999999993), t)), (Zoom * fy((-0.12559999999999993), t)), (Zoom * fz((-0.12559999999999993), t)), t, v_{min}, v_{max}) → M5_{24}
  58. CurveCartesian((Zoom * fx(t, (-0.06241776313844971))), (Zoom * fy(t, (-0.06241776313844971))), (Zoom * fz(t, (-0.06241776313844971))), t, u_{min}, u_{max}) → M4_{25}
  59. CurveCartesian((Zoom * fx((-0.06279999999999997), t)), (Zoom * fy((-0.06279999999999997), t)), (Zoom * fz((-0.06279999999999997), t)), t, v_{min}, v_{max}) → M5_{25}
  60. CurveCartesian((Zoom * fx(t, 3.981633974481369E-4)), (Zoom * fy(t, 3.981633974481369E-4)), (Zoom * fz(t, 3.981633974481369E-4)), t, u_{min}, u_{max}) → M4_{26}
  61. CurveCartesian((Zoom * fx((2.220446049250313 * e) - 16, t)), (Zoom * fy((2.220446049250313 * e) - 16, t)), (Zoom * fz((2.220446049250313 * e) - 16, t)), t, v_{min}, v_{max}) → M5_{26}
  62. CurveCartesian((Zoom * fx(t, 0.06321408993334621)), (Zoom * fy(t, 0.06321408993334621)), (Zoom * fz(t, 0.06321408993334621)), t, u_{min}, u_{max}) → M4_{27}
  63. CurveCartesian((Zoom * fx(0.06280000000000019, t)), (Zoom * fy(0.06280000000000019, t)), (Zoom * fz(0.06280000000000019, t)), t, v_{min}, v_{max}) → M5_{27}
  64. CurveCartesian((Zoom * fx(t, 0.12603001646924405)), (Zoom * fy(t, 0.12603001646924405)), (Zoom * fz(t, 0.12603001646924405)), t, u_{min}, u_{max}) → M4_{28}
  65. CurveCartesian((Zoom * fx(0.12560000000000016, t)), (Zoom * fy(0.12560000000000016, t)), (Zoom * fz(0.12560000000000016, t)), t, v_{min}, v_{max}) → M5_{28}
  66. CurveCartesian((Zoom * fx(t, 0.1888459430051419)), (Zoom * fy(t, 0.1888459430051419)), (Zoom * fz(t, 0.1888459430051419)), t, u_{min}, u_{max}) → M4_{29}
  67. CurveCartesian((Zoom * fx(0.18840000000000012, t)), (Zoom * fy(0.18840000000000012, t)), (Zoom * fz(0.18840000000000012, t)), t, v_{min}, v_{max}) → M5_{29}
  68. CurveCartesian((Zoom * fx(t, 0.25166186954104)), (Zoom * fy(t, 0.25166186954104)), (Zoom * fz(t, 0.25166186954104)), t, u_{min}, u_{max}) → M4_{30}
  69. CurveCartesian((Zoom * fx(0.2512000000000001, t)), (Zoom * fy(0.2512000000000001, t)), (Zoom * fz(0.2512000000000001, t)), t, v_{min}, v_{max}) → M5_{30}
  70. CurveCartesian((Zoom * fx(t, 0.3144777960769378)), (Zoom * fy(t, 0.3144777960769378)), (Zoom * fz(t, 0.3144777960769378)), t, u_{min}, u_{max}) → M4_{31}
  71. CurveCartesian((Zoom * fx(0.3140000000000003, t)), (Zoom * fy(0.3140000000000003, t)), (Zoom * fz(0.3140000000000003, t)), t, v_{min}, v_{max}) → M5_{31}
  72. CurveCartesian((Zoom * fx(t, 0.3772937226128359)), (Zoom * fy(t, 0.3772937226128359)), (Zoom * fz(t, 0.3772937226128359)), t, u_{min}, u_{max}) → M4_{32}
  73. CurveCartesian((Zoom * fx(0.37680000000000025, t)), (Zoom * fy(0.37680000000000025, t)), (Zoom * fz(0.37680000000000025, t)), t, v_{min}, v_{max}) → M5_{32}
  74. CurveCartesian((Zoom * fx(t, 0.44010964914873374)), (Zoom * fy(t, 0.44010964914873374)), (Zoom * fz(t, 0.44010964914873374)), t, u_{min}, u_{max}) → M4_{33}
  75. CurveCartesian((Zoom * fx(0.4396000000000002, t)), (Zoom * fy(0.4396000000000002, t)), (Zoom * fz(0.4396000000000002, t)), t, v_{min}, v_{max}) → M5_{33}
  76. CurveCartesian((Zoom * fx(t, 0.5029255756846316)), (Zoom * fy(t, 0.5029255756846316)), (Zoom * fz(t, 0.5029255756846316)), t, u_{min}, u_{max}) → M4_{34}
  77. CurveCartesian((Zoom * fx(0.5024000000000004, t)), (Zoom * fy(0.5024000000000004, t)), (Zoom * fz(0.5024000000000004, t)), t, v_{min}, v_{max}) → M5_{34}
  78. CurveCartesian((Zoom * fx(t, 0.5657415022205294)), (Zoom * fy(t, 0.5657415022205294)), (Zoom * fz(t, 0.5657415022205294)), t, u_{min}, u_{max}) → M4_{35}
  79. CurveCartesian((Zoom * fx(0.5652000000000001, t)), (Zoom * fy(0.5652000000000001, t)), (Zoom * fz(0.5652000000000001, t)), t, v_{min}, v_{max}) → M5_{35}
  80. CurveCartesian((Zoom * fx(t, 0.6285574287564277)), (Zoom * fy(t, 0.6285574287564277)), (Zoom * fz(t, 0.6285574287564277)), t, u_{min}, u_{max}) → M4_{36}
  81. CurveCartesian((Zoom * fx(0.6280000000000003, t)), (Zoom * fy(0.6280000000000003, t)), (Zoom * fz(0.6280000000000003, t)), t, v_{min}, v_{max}) → M5_{36}
  82. CurveCartesian((Zoom * fx(t, 0.6913733552923256)), (Zoom * fy(t, 0.6913733552923256)), (Zoom * fz(t, 0.6913733552923256)), t, u_{min}, u_{max}) → M4_{37}
  83. CurveCartesian((Zoom * fx(0.6908000000000001, t)), (Zoom * fy(0.6908000000000001, t)), (Zoom * fz(0.6908000000000001, t)), t, v_{min}, v_{max}) → M5_{37}
  84. CurveCartesian((Zoom * fx(t, 0.7541892818282234)), (Zoom * fy(t, 0.7541892818282234)), (Zoom * fz(t, 0.7541892818282234)), t, u_{min}, u_{max}) → M4_{38}
  85. CurveCartesian((Zoom * fx(0.7536000000000003, t)), (Zoom * fy(0.7536000000000003, t)), (Zoom * fz(0.7536000000000003, t)), t, v_{min}, v_{max}) → M5_{38}
  86. CurveCartesian((Zoom * fx(t, 0.8170052083641213)), (Zoom * fy(t, 0.8170052083641213)), (Zoom * fz(t, 0.8170052083641213)), t, u_{min}, u_{max}) → M4_{39}
  87. CurveCartesian((Zoom * fx(0.8164000000000005, t)), (Zoom * fy(0.8164000000000005, t)), (Zoom * fz(0.8164000000000005, t)), t, v_{min}, v_{max}) → M5_{39}
  88. CurveCartesian((Zoom * fx(t, 0.8798211349000191)), (Zoom * fy(t, 0.8798211349000191)), (Zoom * fz(t, 0.8798211349000191)), t, u_{min}, u_{max}) → M4_{40}
  89. CurveCartesian((Zoom * fx(0.8792000000000002, t)), (Zoom * fy(0.8792000000000002, t)), (Zoom * fz(0.8792000000000002, t)), t, v_{min}, v_{max}) → M5_{40}
  90. CurveCartesian((Zoom * fx(t, 0.9426370614359174)), (Zoom * fy(t, 0.9426370614359174)), (Zoom * fz(t, 0.9426370614359174)), t, u_{min}, u_{max}) → M4_{41}
  91. CurveCartesian((Zoom * fx(0.9420000000000004, t)), (Zoom * fy(0.9420000000000004, t)), (Zoom * fz(0.9420000000000004, t)), t, v_{min}, v_{max}) → M5_{41}
  92. CurveCartesian((Zoom * fx(t, 1.0054529879718153)), (Zoom * fy(t, 1.0054529879718153)), (Zoom * fz(t, 1.0054529879718153)), t, u_{min}, u_{max}) → M4_{42}
  93. CurveCartesian((Zoom * fx(1.0048000000000001, t)), (Zoom * fy(1.0048000000000001, t)), (Zoom * fz(1.0048000000000001, t)), t, v_{min}, v_{max}) → M5_{42}
  94. CurveCartesian((Zoom * fx(t, 1.068268914507713)), (Zoom * fy(t, 1.068268914507713)), (Zoom * fz(t, 1.068268914507713)), t, u_{min}, u_{max}) → M4_{43}
  95. CurveCartesian((Zoom * fx(1.0676000000000003, t)), (Zoom * fy(1.0676000000000003, t)), (Zoom * fz(1.0676000000000003, t)), t, v_{min}, v_{max}) → M5_{43}
  96. CurveCartesian((Zoom * fx(t, 1.131084841043611)), (Zoom * fy(t, 1.131084841043611)), (Zoom * fz(t, 1.131084841043611)), t, u_{min}, u_{max}) → M4_{44}
  97. CurveCartesian((Zoom * fx(1.1304000000000005, t)), (Zoom * fy(1.1304000000000005, t)), (Zoom * fz(1.1304000000000005, t)), t, v_{min}, v_{max}) → M5_{44}
  98. CurveCartesian((Zoom * fx(t, 1.1939007675795088)), (Zoom * fy(t, 1.1939007675795088)), (Zoom * fz(t, 1.1939007675795088)), t, u_{min}, u_{max}) → M4_{45}
  99. CurveCartesian((Zoom * fx(1.1932000000000003, t)), (Zoom * fy(1.1932000000000003, t)), (Zoom * fz(1.1932000000000003, t)), t, v_{min}, v_{max}) → M5_{45}
  100. CurveCartesian((Zoom * fx(t, 1.2567166941154067)), (Zoom * fy(t, 1.2567166941154067)), (Zoom * fz(t, 1.2567166941154067)), t, u_{min}, u_{max}) → M4_{46}
  101. CurveCartesian((Zoom * fx(1.2560000000000004, t)), (Zoom * fy(1.2560000000000004, t)), (Zoom * fz(1.2560000000000004, t)), t, v_{min}, v_{max}) → M5_{46}
  102. CurveCartesian((Zoom * fx(t, 1.319532620651305)), (Zoom * fy(t, 1.319532620651305)), (Zoom * fz(t, 1.319532620651305)), t, u_{min}, u_{max}) → M4_{47}
  103. CurveCartesian((Zoom * fx(1.3188000000000002, t)), (Zoom * fy(1.3188000000000002, t)), (Zoom * fz(1.3188000000000002, t)), t, v_{min}, v_{max}) → M5_{47}
  104. CurveCartesian((Zoom * fx(t, 1.3823485471872028)), (Zoom * fy(t, 1.3823485471872028)), (Zoom * fz(t, 1.3823485471872028)), t, u_{min}, u_{max}) → M4_{48}
  105. CurveCartesian((Zoom * fx(1.3816000000000004, t)), (Zoom * fy(1.3816000000000004, t)), (Zoom * fz(1.3816000000000004, t)), t, v_{min}, v_{max}) → M5_{48}
  106. CurveCartesian((Zoom * fx(t, 1.4451644737231006)), (Zoom * fy(t, 1.4451644737231006)), (Zoom * fz(t, 1.4451644737231006)), t, u_{min}, u_{max}) → M4_{49}
  107. CurveCartesian((Zoom * fx(1.4444000000000001, t)), (Zoom * fy(1.4444000000000001, t)), (Zoom * fz(1.4444000000000001, t)), t, v_{min}, v_{max}) → M5_{49}
  108. CurveCartesian((Zoom * fx(t, 1.5079804002589985)), (Zoom * fy(t, 1.5079804002589985)), (Zoom * fz(t, 1.5079804002589985)), t, u_{min}, u_{max}) → M4_{50}
  109. CurveCartesian((Zoom * fx(1.5072000000000003, t)), (Zoom * fy(1.5072000000000003, t)), (Zoom * fz(1.5072000000000003, t)), t, v_{min}, v_{max}) → M5_{50}
  110. CurveCartesian((Zoom * fx(t, 1.5707963267948963)), (Zoom * fy(t, 1.5707963267948963)), (Zoom * fz(t, 1.5707963267948963)), t, u_{min}, u_{max}) → M4_{51}
  111. CurveCartesian((Zoom * fx(1.5700000000000005, t)), (Zoom * fy(1.5700000000000005, t)), (Zoom * fz(1.5700000000000005, t)), t, v_{min}, v_{max}) → M5_{51}

AI 绘图提示语参考

绘制罗马曲面的网格效果，使用参数化方程定义曲面，通过调整参数观察曲面变化。首先输入参数u和v的最小值和最大值，然后输入x、y、z的函数表达式，最后设置缩放因子绘制曲面，并在特定参数下绘制曲线，形成网格效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。