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Contour Plot Guide

Contour Plot Guide
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2015-05-18 18:44
FunctionGraphing
In collections surface 3D /3D-Oberflächen 1 My 3D Collection
This example demonstrates how to create contour plots for arbitrary functions z=f(x,y). Key mathematical concepts include function graphs, contour lines, and coordinate systems. Construction involves GeoGebra commands like Polygon, Segment, RemoveUndefined, etc. Suitable for high school students or college freshmen learning function visualization and spatial geometry.

GeoGebra Commands & Parameters

  1. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, b, c, d, e
  2. Segment(B02, B01) → a
  3. RemoveUndefined(Join[Zip[Mirror[{Roots[f0(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, Sequence[x_{min} + ((x_{max} - x_{min}) / N_P * i), i, 0, N_P]]]) → P1xxy
  4. RemoveUndefined(Join[Zip[Reverse[{Roots[f0(x, a), x_{min}, x_{max}]}] + (0, a), a, Sequence[y_{min} + ((y_{max} - y_{min}) / N_P * i), i, 0, N_P]]]) → P2yyx
  5. Textfield(v_1) → inputBox2
  6. Textfield(f) → inputBox3
  7. Textfield(N_C) → inputBox1
  8. Textfield(x_{min}) → inputBox4
  9. Textfield(x_{max}) → inputBox5
  10. Textfield(y_{max}) → inputBox6
  11. Textfield(z_{max}) → inputBox7
  12. Textfield(y_{min}) → inputBox8
  13. Textfield(z_{min}) → inputBox9
  14. PointIn(poly1) → PTest
  15. Point(a, 1 - zzii_B) → A
  16. Textfield(N_P) → inputBox10
  17. Sum(Sequence[If[f0(x(PTest), y(PTest)) - f0(x(Element[lr01, i]), y(Element[lr01, i])) > 0, 1, 0], i, 1, 11]) → ext1
  18. Zip((x(a), y(a), z0), a, Join[{P1xxy, P2yyx}]) → list1
  19. Length(list1) → Lä
  20. Textfield(v) → inputBox11
  21. Textfield(step) → inputBox12
  22. Sequence(Element[list1, i], i, k, k + step) → M01
  23. Function(f(a, b), a, x_{min} - 0.2, x_{max} + 0.2, b, y_{min} - 0.2, y_{max} + 0.2) → g