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曲面拟合

曲面拟合
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2020-06-20 15:44
解析几何最值优化
①本范例演示如何通过点集数据拟合三维曲面；②涉及的核心数学概念包括曲面拟合、几何分布、单位圆、不等式和旋转；③作图要点：使用PointIn、Point、Sequence、FitPoly、Coefficients、Surface、CurveCartesian等命令创建和拟合曲面；④适合高中及以上学生学习和理解数据拟合与三维几何。

GeoGebra 命令及参数

  1. PointIn(Plane[A, Plane[xAxis, zAxis]]) → B
  2. PointIn(Plane[A, Plane[xAxis, zAxis]]) → C
  3. PointIn(Plane[A, Plane[xAxis, zAxis]]) → D
  4. PointIn(Plane[A, Plane[yAxis, zAxis]]) → E
  5. Point(IntersectPath[Plane[B, Plane[yAxis, zAxis]], Plane[E, Plane[xAxis, zAxis]]]) → F
  6. Point(IntersectPath[Plane[C, Plane[yAxis, zAxis]], Plane[E, Plane[xAxis, zAxis]]]) → G
  7. Point(IntersectPath[Plane[D, Plane[yAxis, zAxis]], Plane[E, Plane[xAxis, zAxis]]]) → H
  8. PointIn(Plane[A, Plane[yAxis, zAxis]]) → I
  9. PointIn(Plane[A, Plane[yAxis, zAxis]]) → M
  10. Point(IntersectPath[Plane[B, Plane[yAxis, zAxis]], Plane[I, Plane[xAxis, zAxis]]]) → J
  11. Point(IntersectPath[Plane[C, Plane[yAxis, zAxis]], Plane[I, Plane[xAxis, zAxis]]]) → K
  12. Point(IntersectPath[Plane[D, Plane[yAxis, zAxis]], Plane[I, Plane[xAxis, zAxis]]]) → L
  13. Point(IntersectPath[Plane[B, Plane[yAxis, zAxis]], Plane[M, Plane[xAxis, zAxis]]]) → N
  14. Point(IntersectPath[Plane[C, Plane[yAxis, zAxis]], Plane[M, Plane[xAxis, zAxis]]]) → O
  15. Point(IntersectPath[Plane[D, Plane[yAxis, zAxis]], Plane[M, Plane[xAxis, zAxis]]]) → P
  16. Sequence((x(Element[la, i]), z(Element[la, i])), i, 1, 4) → lax
  17. Sequence((x(Element[le, i]), z(Element[le, i])), i, 1, 4) → lex
  18. Sequence((x(Element[li, i]), z(Element[li, i])), i, 1, 4) → lix
  19. Sequence((x(Element[lm, i]), z(Element[lm, i])), i, 1, 4) → lmx
  20. FitPoly(lax, 3) → fax
  21. FitPoly(lex, 3) → fex
  22. FitPoly(lix, 3) → fix
  23. FitPoly(lmx, 3) → fmx
  24. Coefficients(fax) → cax
  25. Coefficients(fex) → cex
  26. Coefficients(fix) → cix
  27. Coefficients(fmx) → cmx
  28. FitPoly(lcy3, 3) → fy3
  29. FitPoly(lcy2, 3) → fy2
  30. FitPoly(lcy1, 3) → fy1
  31. FitPoly(lcy0, 3) → fy0
  32. Surface(u, v, f(u, v), u, x(A), x(D), v, y(A), y(M)) → a
  33. CurveCartesian(t, y(E), fex(t), t, x(A), x(D)) → ce
  34. CurveCartesian(t, y(I), fix(t), t, x(A), x(D)) → ci
  35. CurveCartesian(t, y(A), fax(t), t, x(A), x(D)) → ca
  36. CurveCartesian(t, y(M), fmx(t), t, x(A), x(D)) → cm
  37. CurveCartesian(x(A), t, f(x(A), t), t, y(A), y(M)) → caa
  38. CurveCartesian(x(B), t, f(x(B), t), t, y(A), y(M)) → cb
  39. CurveCartesian(x(C), t, f(x(C), t), t, y(A), y(M)) → cc
  40. CurveCartesian(x(D), t, f(x(D), t), t, y(A), y(M)) → cd
  41. Surface(u, v, f(u, v), u, A1, A2, v, y(A), y(M)) → B1
  42. Surface(u, v, f(u, v), u, A2, A3, v, y(A), y(M)) → B2
  43. Surface(u, v, f(u, v), u, A3, A4, v, y(A), y(M)) → B3
  44. Surface(u, v, f(u, v), u, A4, A5, v, y(A), y(M)) → B4
  45. Surface(u, v, f(u, v), u, A5, A6, v, y(A), y(M)) → B5
  46. Surface(u, v, f(u, v), u, A6, A7, v, y(A), y(M)) → B6
  47. Surface(u, v, f(u, v), u, A7, A8, v, y(A), y(M)) → B7
  48. Surface(u, v, f(u, v), u, A8, A9, v, y(A), y(M)) → B8
  49. Surface(u, v, f(u, v), u, A9, A10, v, y(A), y(M)) → B9
  50. Surface(u, v, f(u, v), u, A10, A11, v, y(A), y(M)) → B10
  51. Surface(u, v, f(u, v), u, A11, A12, v, y(A), y(M)) → B11
  52. Surface(u, v, f(u, v), u, A12, A13, v, y(A), y(M)) → B12
  53. Surface(u, v, f(u, v), u, A13, A14, v, y(A), y(M)) → B13
  54. Surface(u, v, f(u, v), u, A14, A15, v, y(A), y(M)) → B14
  55. Surface(u, v, f(u, v), u, A15, A16, v, y(A), y(M)) → B15
  56. Surface(u, v, f(u, v), u, A16, A17, v, y(A), y(M)) → B16
  57. Surface(u, v, f(u, v), u, A17, A18, v, y(A), y(M)) → B17
  58. Surface(u, v, f(u, v), u, A18, A19, v, y(A), y(M)) → B18
  59. Surface(u, v, f(u, v), u, A19, A20, v, y(A), y(M)) → B19
  60. Surface(u, v, f(u, v), u, A20, A21, v, y(A), y(M)) → B20
  61. Surface(u, v, f(u, v), u, A21, A22, v, y(A), y(M)) → B21
  62. Surface(u, v, f(u, v), u, A22, A23, v, y(A), y(M)) → B22
  63. Surface(u, v, f(u, v), u, A23, A24, v, y(A), y(M)) → B23
  64. Surface(u, v, f(u, v), u, A24, A25, v, y(A), y(M)) → B24
  65. Surface(u, v, f(u, v), u, A25, A26, v, y(A), y(M)) → B25
  66. Surface(u, v, f(u, v), u, A26, A27, v, y(A), y(M)) → B26
  67. Surface(u, v, f(u, v), u, A27, A28, v, y(A), y(M)) → B27
  68. Surface(u, v, f(u, v), u, A28, A29, v, y(A), y(M)) → B28
  69. Surface(u, v, f(u, v), u, A29, A30, v, y(A), y(M)) → B29
  70. Surface(u, v, f(u, v), u, A30, A31, v, y(A), y(M)) → B30
  71. Surface(u, v, f(u, v), u, A31, A32, v, y(A), y(M)) → B31
  72. Surface(u, v, f(u, v), u, A32, A33, v, y(A), y(M)) → B32
  73. Surface(u, v, f(u, v), u, A33, A34, v, y(A), y(M)) → B33
  74. Surface(u, v, f(u, v), u, A34, A35, v, y(A), y(M)) → B34
  75. Surface(u, v, f(u, v), u, A35, A36, v, y(A), y(M)) → B35
  76. Surface(u, v, f(u, v), u, A36, A37, v, y(A), y(M)) → B36
  77. Surface(u, v, f(u, v), u, A37, A38, v, y(A), y(M)) → B37
  78. Surface(u, v, f(u, v), u, A38, A39, v, y(A), y(M)) → B38
  79. Surface(u, v, f(u, v), u, A39, A40, v, y(A), y(M)) → B39
  80. Surface(u, v, f(u, v), u, A40, A41, v, y(A), y(M)) → B40
  81. Surface(u, v, f(u, v), u, A41, A42, v, y(A), y(M)) → B41
  82. Surface(u, v, f(u, v), u, A42, A43, v, y(A), y(M)) → B42
  83. Surface(u, v, f(u, v), u, A43, A44, v, y(A), y(M)) → B43
  84. Surface(u, v, f(u, v), u, A44, A45, v, y(A), y(M)) → B44
  85. Surface(u, v, f(u, v), u, A45, A46, v, y(A), y(M)) → B45
  86. Surface(u, v, f(u, v), u, A46, A47, v, y(A), y(M)) → B46
  87. Surface(u, v, f(u, v), u, A47, A48, v, y(A), y(M)) → B47
  88. Surface(u, v, f(u, v), u, A48, A49, v, y(A), y(M)) → B48
  89. Surface(u, v, f(u, v), u, A49, A50, v, y(A), y(M)) → B49
  90. Surface(u, v, f(u, v), u, A50, A51, v, y(A), y(M)) → B50
  91. Surface(u, v, f(u, v), u, A51, A52, v, y(A), y(M)) → B51

AI 绘图提示语参考

绘制一个通过一组数据点的曲面，首先在指定平面上创建点A、B、C、D、E、F、G、H、I、M，然后通过这些点生成一系列路径交点，接着使用这些路径交点拟合多项式函数，最后利用拟合的多项式函数绘制曲面，包括从点A到点M的路径以及从点A到点D的路径。
以上提示语为根据原始绘图命令整理而来，仅供参考。