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Voronoi Diffusion View

Voronoi Diffusion View
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2020-04-24 15:15
FunctionCoordinate GeometryParametric EquationGeometric Construction
This example demonstrates the diffusion effect and morphological changes of Voronoi diagrams under varying parameters. Core mathematical concepts include parametric curves, confidence intervals, integers, polynomial functions, hyperbolas, and similarity transformations. Construction highlights involve commands like Sequence, Translate, Line, Join, Voronoi, Parabola, Point, and Polygon from GeoGebra. Suitable for high school and above students to understand polygon partitioning, parametric equations, and the application of transformations in geometry.

GeoGebra Commands & Parameters

  1. Sequence((x(A) + (b * sin((w * i))), y(A) + i), i, (-2 * π), (2 * π), (2 * π / n)) → l1
  2. Sequence(Translate[Element[l1, i], Vector[(a * Vector[A, A + (-1, 0)])]], i, 1, Length[l1]) → l2
  3. Translate(l2, Vector[A, A + (20, 0)]) → l2'_1
  4. Translate(l2, Vector[A, A + (10, 0)]) → l2'
  5. Line(B, yAxis) → f
  6. Join({l2, l3, l2', l2'_1}) → l4
  7. Voronoi(l4) → graphe2
  8. Parabola(F, f) → c
  9. Sequence(Parabola[Element[l2, i], f], i, 1, Length[l2]) → l5
  10. Point(f) → P
  11. Polygon(B, Q, R, P) → q1, b_1, q, r, p