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使用轨迹法绘制彩色参数曲面

使用轨迹法绘制彩色参数曲面
几何画板及绘图内容加载中，请稍等……
2015-07-20 19:11
函数解析几何立体几何参数方程函数图像
这个范例演示了如何使用轨迹法绘制带有RGB颜色的参数曲面。核心数学概念包括参数方程和颜色映射。构造过程中使用了Sequence, Join, Zip, RemoveUndefined, Max, Min, Surface, CurveCartesian, Textfield, Point等命令。适合高中及以上学生或教师使用，用于教学或研究参数曲面的可视化。

GeoGebra 命令及参数

  1. Sequence(Sequence[(u_{min} + (i * dx), v_{min} + (j * dy)), i, 0, Na], j, 0, Na) → l1a
  2. Join(l1a) → uv
  3. Zip(fz(a, b), a, u0, b, v0) → Z1
  4. Zip(fy(a, b), a, u0, b, v0) → Y1
  5. Zip(fx(a, b), a, u0, b, v0) → X1
  6. RemoveUndefined(X1) → X1E
  7. Max(X1E) → x1maxa
  8. Min(X1E) → x1mina
  9. RemoveUndefined(Y1) → Y1E
  10. Max(Y1E) → x2maxa
  11. Min(Y1E) → x2mina
  12. RemoveUndefined(Z1) → Z1E
  13. Max(Z1E) → x3maxa
  14. Min(Z1E) → x3mina
  15. Surface((((r_X * 5) * cos(u)) * sin(v)), (((r_Y * 5) * sin(u)) * sin(v)), ((r_Z * 5) * (cos(v) + log(tan(v / 2)))) + (1.3 * u), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → h
  16. CurveCartesian((fx(t, a_v) * r_X), (fy(t, a_v) * r_Y), (fz(t, a_v) * r_Z), t, u_{min}, u_{max}) → f_u
  17. CurveCartesian((fx(a_u, t) * r_X), (fy(a_u, t) * r_Y), (fz(a_u, t) * r_Z), t, v_{min}, v_{max}) → f_v
  18. Textfield(u_{min}) → inputBox4
  19. Textfield(u_{max}) → inputBox5
  20. Textfield(v_{min}) → inputBox6
  21. Textfield(v_{max}) → inputBox7
  22. Textfield(Pstyle) → Textfeld1
  23. Textfield(Nx) → Textfeld2
  24. Textfield(v_u) → Textfeld3
  25. Textfield(v_v) → Textfeld4
  26. Textfield(r_X) → inputBox8
  27. Textfield(r_Y) → inputBox9
  28. Textfield(r_Z) → inputBox10
  29. Point(f_u, 0) → Pr_{0}
  30. Point(f_u, 0.02) → Pr_{1}
  31. Point(f_u, 0.04) → Pr_{2}
  32. Point(f_u, 0.06) → Pr_{3}
  33. Point(f_u, 0.08) → Pr_{4}
  34. Point(f_u, 0.1) → Pr_{5}
  35. Point(f_u, 0.12) → Pr_{6}
  36. Point(f_u, 0.14) → Pr_{7}
  37. Point(f_u, 0.16) → Pr_{8}
  38. Point(f_u, 0.18) → Pr_{9}
  39. Point(f_u, 0.2) → Pr_{10}
  40. Point(f_u, 0.22) → Pr_{11}
  41. Point(f_u, 0.24) → Pr_{12}
  42. Point(f_u, 0.26) → Pr_{13}
  43. Point(f_u, 0.28) → Pr_{14}
  44. Point(f_u, 0.3) → Pr_{15}
  45. Point(f_u, 0.32) → Pr_{16}
  46. Point(f_u, 0.34) → Pr_{17}
  47. Point(f_u, 0.36) → Pr_{18}
  48. Point(f_u, 0.38) → Pr_{19}
  49. Point(f_u, 0.4) → Pr_{20}
  50. Point(f_u, 0.42) → Pr_{21}
  51. Point(f_u, 0.44) → Pr_{22}
  52. Point(f_u, 0.46) → Pr_{23}
  53. Point(f_u, 0.48) → Pr_{24}
  54. Point(f_u, 0.5) → Pr_{25}
  55. Point(f_u, 0.52) → Pr_{26}
  56. Point(f_u, 0.54) → Pr_{27}
  57. Point(f_u, 0.56) → Pr_{28}
  58. Point(f_u, 0.58) → Pr_{29}
  59. Point(f_u, 0.6) → Pr_{30}
  60. Point(f_u, 0.62) → Pr_{31}
  61. Point(f_u, 0.64) → Pr_{32}
  62. Point(f_u, 0.66) → Pr_{33}
  63. Point(f_u, 0.68) → Pr_{34}
  64. Point(f_u, 0.7) → Pr_{35}
  65. Point(f_u, 0.72) → Pr_{36}
  66. Point(f_u, 0.74) → Pr_{37}
  67. Point(f_u, 0.76) → Pr_{38}
  68. Point(f_u, 0.78) → Pr_{39}
  69. Point(f_u, 0.8) → Pr_{40}
  70. Point(f_u, 0.82) → Pr_{41}
  71. Point(f_u, 0.84) → Pr_{42}
  72. Point(f_u, 0.86) → Pr_{43}
  73. Point(f_u, 0.88) → Pr_{44}
  74. Point(f_u, 0.9) → Pr_{45}
  75. Point(f_u, 0.92) → Pr_{46}
  76. Point(f_u, 0.94) → Pr_{47}
  77. Point(f_u, 0.96) → Pr_{48}
  78. Point(f_u, 0.98) → Pr_{49}
  79. Point(f_u, 1) → Pr_{50}
  80. Point(f_v, 0) → Pr_{51}
  81. Point(f_v, 0.02) → Pr_{52}
  82. Point(f_v, 0.04) → Pr_{53}
  83. Point(f_v, 0.06) → Pr_{54}
  84. Point(f_v, 0.08) → Pr_{55}
  85. Point(f_v, 0.1) → Pr_{56}
  86. Point(f_v, 0.12) → Pr_{57}
  87. Point(f_v, 0.14) → Pr_{58}
  88. Point(f_v, 0.16) → Pr_{59}
  89. Point(f_v, 0.18) → Pr_{60}
  90. Point(f_v, 0.2) → Pr_{61}
  91. Point(f_v, 0.22) → Pr_{62}
  92. Point(f_v, 0.24) → Pr_{63}
  93. Point(f_v, 0.26) → Pr_{64}
  94. Point(f_v, 0.28) → Pr_{65}
  95. Point(f_v, 0.3) → Pr_{66}
  96. Point(f_v, 0.32) → Pr_{67}
  97. Point(f_v, 0.34) → Pr_{68}
  98. Point(f_v, 0.36) → Pr_{69}
  99. Point(f_v, 0.38) → Pr_{70}
  100. Point(f_v, 0.4) → Pr_{71}
  101. Point(f_v, 0.42) → Pr_{72}
  102. Point(f_v, 0.44) → Pr_{73}
  103. Point(f_v, 0.46) → Pr_{74}
  104. Point(f_v, 0.48) → Pr_{75}
  105. Point(f_v, 0.5) → Pr_{76}
  106. Point(f_v, 0.52) → Pr_{77}
  107. Point(f_v, 0.54) → Pr_{78}
  108. Point(f_v, 0.56) → Pr_{79}
  109. Point(f_v, 0.58) → Pr_{80}
  110. Point(f_v, 0.6) → Pr_{81}
  111. Point(f_v, 0.62) → Pr_{82}
  112. Point(f_v, 0.64) → Pr_{83}
  113. Point(f_v, 0.66) → Pr_{84}
  114. Point(f_v, 0.68) → Pr_{85}
  115. Point(f_v, 0.7) → Pr_{86}
  116. Point(f_v, 0.72) → Pr_{87}
  117. Point(f_v, 0.74) → Pr_{88}
  118. Point(f_v, 0.76) → Pr_{89}
  119. Point(f_v, 0.78) → Pr_{90}
  120. Point(f_v, 0.8) → Pr_{91}
  121. Point(f_v, 0.82) → Pr_{92}
  122. Point(f_v, 0.84) → Pr_{93}
  123. Point(f_v, 0.86) → Pr_{94}
  124. Point(f_v, 0.88) → Pr_{95}
  125. Point(f_v, 0.9) → Pr_{96}
  126. Point(f_v, 0.92) → Pr_{97}
  127. Point(f_v, 0.94) → Pr_{98}
  128. Point(f_v, 0.96) → Pr_{99}
  129. Point(f_v, 0.98) → Pr_{100}
  130. Point(f_v, 1) → Pr_{101}
  131. Textfield(fx) → inputBox1
  132. Textfield(fy) → inputBox2
  133. Textfield(fz) → inputBox3

AI 绘图提示语参考

绘制一个带颜色映射的参数曲面，曲面由 u、v 两参数定义，x = r_X·5·cos(u)·sin(v)，y = r_Y·5·sin(u)·sin(v)，z = r_Z·5·(cos(v)+ln(tan(v/2)))+1.3·u；在曲面上显示两族参数线（固定 v 的 u 线与固定 u 的 v 线），并沿一条 u 线放置一系列等距追踪点；提供 u_min、u_max、v_min、v_max、r_X、r_Y、r_Z 等参数的输入框以便交互调整。
以上提示语为根据原始绘图命令整理而来，仅供参考。