MathPlotAI Logo MathPlotAI

Intersection Points of Implicit Curves Scanning Method

Intersection Points of Implicit Curves Scanning Method
Loading the math board and drawing, please wait…
2016-12-03 19:07
FunctionCoordinate GeometryOptimizationGraphing
This example demonstrates how to find intersection points of two implicit curves using a scanning method. Key math concepts include implicit curves, intersection calculations, and scanning method principles. GeoGebra commands and objects used in the construction are Textfield, RemoveUndefined, Zip, TableText, ImplicitCurve, Polygon, etc. Suitable for high school and above students to understand implicit curve intersection solving methods and programming concepts.

GeoGebra Commands & Parameters

  1. Textfield(Nn) → InputBox4
  2. Textfield(e) → InputBox5
  3. Textfield(x_{min}) → InputBox6
  4. Textfield(x_{max}) → InputBox7
  5. Textfield(y_{min}) → InputBox8
  6. Textfield(y_{max}) → InputBox9
  7. RemoveUndefined(Join[Sequence[Zip[a + (0, y_{min} + (dy2 * (s0 - 1))), a, {Roots[f01(x, y_{min} + (dy2 * (s0 - 1))), x_{min}, x_{max}]}], s0, 1, Nn + 1]]) → Rootsxy
  8. RemoveUndefined(Join[Sequence[Zip[a + (0, x_{min} + (dx2 * (s0 - 1))), a, {Roots[f01(x_{min} + (dx2 * (s0 - 1)), x), y_{min}, y_{max}]}], s0, 1, Nn + 1]]) → Rootsyx
  9. RemoveUndefined(KeepIf[abs(f2(x(A), y(A))) ≤ e, A, Rootsxy]) → listxy_0
  10. RemoveUndefined(KeepIf[abs(f2(y(A), x(A))) ≤ e, A, Rootsyx]) → listyx_0
  11. Zip((x(a), y(a)), a, listxy_0) → listxya_0
  12. Zip((y(a), x(a)), a, listyx_0) → listyxa_0
  13. TableText({Join[{{"Roots_{yx}"}, listyxa_0}]}, "vr") → text34
  14. TableText({Join[{{"Roots_{xy}"}, listxya_0}]}, "vr") → text23
  15. Textfield(α) → InputBox2
  16. ImplicitCurve(f1(x, y)) → a
  17. ImplicitCurve(f2(x, y)) → b
  18. ImplicitCurve(f01(x, y)) → c
  19. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, f, g, h, i
  20. Textfield(f1) → InputBox1
  21. Textfield(f2) → InputBox3
  22. RemoveUndefined(Zip[(x(a), y(a)), a, Join[{listxya_0, listyxa_0}]]) → listxyres0
  23. Textfield(t) → InputBox10

AI Drawing Prompt Reference

Draw the intersection points of two implicit curves using a scanning method. Set parameter ranges and an error threshold, then find intersection points within the specified range and connect those that meet the criteria. Finally, plot the two implicit curves and the bounding rectangle of the parameters, labeling all intersection points with their coordinates.
The prompt above was compiled from the original drawing commands and is for reference only.