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三次曲面拟合

三次曲面拟合
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2015-06-18 01:19
函数解析几何
所属专题 surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1 surface 3D surface 3D
①本范例演示了如何使用 GeoGebra 进行三次曲面拟合，展示数据与拟合曲面的关系；②涉及的核心数学概念包括曲面拟合、多项式回归、系数分析；③作图要点：使用了 PointIn, Point, Sequence, FitPoly, Coefficients, Surface, CurveCartesian 等命令和对象来创建数据点、拟合曲面和显示系数；④适合高中及以上学生学习和理解数据拟合、多项式函数及三维图形的构建。

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

AI 绘图提示语参考

绘制一个三维图形，展示数据点与三次曲面拟合的关系。首先创建多个数据点，然后通过三次多项式回归拟合这些点生成曲面。接着，提取并显示拟合曲面的系数，最后用曲线连接相关点，清晰展示数据与曲面、系数之间的联系。
以上提示语为根据原始绘图命令整理而来，仅供参考。