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Equiangular Spiral, Voronoi and Delaunay Patterns

Equiangular Spiral, Voronoi and Delaunay Patterns
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2018-10-02 20:41
Coordinate GeometryGeometric Construction
In collections Developing games and puzzles with 3D printing for STEAM
This example demonstrates the generation and visualization of equiangular spirals, Voronoi diagrams, and Delaunay triangulations. Key math concepts include equiangular spirals, Voronoi diagrams, Delaunay triangulation, sequences, and coordinate geometry. It is constructed using GeoGebra commands like Sequence, Voronoi, Rotate, DelaunayTriangulation, Line, Point, PolyLine, Polygon, and Intersect. Suitable for high school and above students to learn spatial geometry, discrete mathematics, and computational geometry.

GeoGebra Commands & Parameters

  1. Sequence((((r * log(i)) * cos(((2 * π / d) * i))), ((r * log(i)) * sin(((2 * π / d) * i)))), i, 1, n) → l2
  2. Voronoi(l2) → v2
  3. Rotate(l2, π / 180, (0, 0)) → l1
  4. Voronoi(l1) → v1
  5. DelauneyTriangulation(l1) → d1
  6. Line(A, xAxis) → f
  7. Point(f) → B
  8. Rotate(B, π / 2, A) → C
  9. PolyLine(A, B, D, C, A) → g
  10. Polygon({A, B, D, C}) → a
  11. Intersect(d = (1.1 * r), d = 0.73) → G

AI Drawing Prompt Reference

Draw a graph generated by an equiangular spiral, then create a Voronoi diagram and Delaunay triangulation on it. Ensure clear connections between the spiral, Voronoi regions, and triangulation triangles. The overall layout should be clear and easy to understand, suitable for learning spatial geometry and discrete mathematics.
The prompt above was compiled from the original drawing commands and is for reference only.