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Cubic Surface Fitting

Cubic Surface Fitting
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2015-06-18 01:19
FunctionCoordinate Geometry
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1 surface 3D surface 3D
This example demonstrates how to perform cubic surface fitting using GeoGebra, illustrating the relationship between data and the fitted surface. Key math concepts include surface fitting, polynomial regression, and coefficient analysis. Construction highlights involve commands like PointIn, Point, Sequence, FitPoly, Coefficients, Surface, and CurveCartesian for creating data points, fitting surfaces, and displaying coefficients. Suitable for high school and above students learning data fitting, polynomial functions, and 3D graphing.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a 3D visualization showing the relationship between data points and a cubic surface fitted using polynomial regression. Generate multiple data points, fit a cubic surface through them, extract and display the coefficients of the fitted surface, and connect relevant points with curves to illustrate the connection between data, surface, and coefficients.
The prompt above was compiled from the original drawing commands and is for reference only.