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Voronoi by inflating spheres

Voronoi by inflating spheres
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2017-12-13 22:10
FunctionCoordinate GeometrySolid Geometry
This example demonstrates creating Voronoi diagrams by inflating spheres. It involves core mathematical concepts like spheres, function graphs, hypergeometric distribution, parallelograms, rotation, and real numbers. Construction highlights include using commands like Sphere and IntersectConic from GeoGebra. Suitable for high school and above, exploring spatial distribution and parametric design of Voronoi patterns.

GeoGebra Commands & Parameters

  1. Sphere((x(A), y(A), (-a)), A) → b
  2. Sphere((x(B), y(B), (-a)), B) → c
  3. Sphere((x(C), y(C), (-a)), C) → d
  4. IntersectConic(b, c) → e
  5. IntersectConic(c, d) → f
  6. IntersectConic(b, d) → g
  7. Sphere((x(D), y(D), (-a)), D) → h
  8. IntersectConic(d, h) → k
  9. IntersectConic(h, c) → p
  10. IntersectConic(h, b) → q
  11. Sphere((x(E), y(E), (-a)), E) → i
  12. IntersectConic(i, h) → r
  13. IntersectConic(d, i) → s
  14. IntersectConic(c, i) → t
  15. IntersectConic(c, h) → c_1