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Hausdorff Distance Demo

Hausdorff Distance Demo
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2014-05-26 21:03
FunctionTrigonometryCoordinate GeometryOptimizationGeometric Construction
This example demonstrates the Hausdorff distance between two sets, illustrating the calculation method through dynamic figures; core math concepts include Hausdorff metric, distance computation, set theory; construction highlights involve commands/objects like Polygon, Circle, Tangent, Intersect, Segment, Max, Textfield in GeoGebra; suitable for high school and above learners to understand the application of Hausdorff metric in fractal geometry and graphics.

GeoGebra Commands & Parameters

  1. Polygon(A1, B1, C1, D1, E1) → poly1, a1, b1, c1, d1, e1
  2. Polygon(A2, B2, C2, D2, E2) → poly2, a2, b2, c2, d2, e2
  3. Circle(A1, r1) → sa1
  4. Circle(B1, r1) → sb1
  5. Circle(C1, r1) → sc1
  6. Circle(D1, r1) → sd1
  7. Circle(E1, r1) → se1
  8. Tangent(d1, sd1) → dd1, ddd1
  9. Intersect(se1, ddd1) → TED1,
  10. Intersect(sd1, ddd1) → TDE1
  11. Segment(TED1, TDE1) → de1
  12. Tangent(c1, sc1) → cc1, ccc1
  13. Intersect(sc1, ccc1) → TCD1
  14. Intersect(sd1, ccc1) → TDC1, D
  15. Segment(TCD1, TDC1) → cd1
  16. Tangent(b1, sb1) → bb1, bbb1
  17. Intersect(sb1, bbb1) → TBC1
  18. Intersect(sc1, bbb1) → TCB1, C
  19. Segment(TBC1, TCB1) → bc1
  20. Tangent(a1, sa1) → aa1, aaa1
  21. Intersect(sa1, aaa1, 1) → TAB1
  22. Intersect(sb1, aaa1, 1) → TBA1
  23. Segment(TAB1, TBA1) → ab1
  24. Tangent(e1, se1) → ee1, eee1
  25. Intersect(sa1, eee1, 1) → TAE1
  26. Intersect(se1, eee1, 1) → TEA1
  27. Segment(TAE1, TEA1) → ea1
  28. Circle(A2, r2) → sa2
  29. Circle(B2, r2) → sb2
  30. Circle(C2, r2) → sc2
  31. Circle(D2, r2) → sd2
  32. Circle(E2, r2) → se2
  33. Tangent(d2, sd2) → dd2, ddd2
  34. Intersect(sd2, ddd2) → TDE2
  35. Intersect(se2, ddd2) → TED2,
  36. Segment(TDE2, TED2) → de2
  37. Tangent(c2, sc2) → cc2, ccc2
  38. Intersect(sc2, ccc2) → TCD2
  39. Intersect(sd2, ccc2) → TDC2,
  40. Segment(TCD2, TDC2) → cd2
  41. Tangent(b2, sb2) → bb2, bbb2
  42. Intersect(sb2, bbb2) → TBC2
  43. Intersect(sc2, bbb2) → TCB2, A
  44. Segment(TBC2, TCB2) → bc2
  45. Tangent(a2, sa2) → aa2, aaa2
  46. Intersect(sa2, aaa2) → TAB2
  47. Intersect(sb2, aaa2) → TBA2, B
  48. Segment(TAB2, TBA2) → ab2
  49. Tangent(e2, se2) → ee2, eee2
  50. Intersect(sa2, eee2) → TAE2, E
  51. Intersect(se2, eee2) → TEA2
  52. Segment(TAE2, TEA2) → ea2
  53. Max(r1, r2) → dH
  54. Textfield(dH) → poleTekstowe1

AI Drawing Prompt Reference

Draw two polygons, draw circles with the same radius for each vertex, and draw tangents from the centers of the circles. Connect the intersection points of the tangents with the circles to form new segments, ultimately displaying the intersections and segments of two groups to illustrate the Hausdorff distance calculation method between sets.
The prompt above was compiled from the original drawing commands and is for reference only.