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Spline's Cube Decorations

Spline's Cube Decorations
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2019-02-13 18:16
FunctionSolid GeometryTransformationParametric EquationGeometric Construction
In collections Color 3D surfaces
This example demonstrates the creation of intricate cube decorations using spline curves and geometric transformations. Key math concepts include solid geometry, transformation geometry, parametric equations, and function interpolation. GeoGebra commands like Join, Spline, Sequence, Polygon, Circle, Translate, and Sphere are used to construct the patterns. Suitable for high school and above students exploring applications of spatial geometry and parametric curves.

GeoGebra Commands & Parameters

  1. Join({Sequence[(cos(i), sin(i)), i, 0, 6.283185307179586, (2 * π / m)], {(1 + d, 0), (1 + d, -1 - d), (-1 - d, -1 - d), (-1 - d, 1 + d), (1 + d, 1 + d), (1 + d, 0)}}) → liste6
  2. Spline(liste1, 3) → a
  3. Sequence((cos(i), sin(i)), i, 0, (2 * π / n), (2 * π / ((n * m)))) → liste3
  4. Sequence(Point[a, i], i, 0, 1 - 1 / m, 1 / m) → liste2
  5. Sequence(Point[Rotate[a, (2 * π / n)], 1 - i], i, 1 / m, 1, 1 / m) → liste4
  6. Polygon(Join[{liste2, liste3, liste4}]) → poly1
  7. Polygon(liste6) → poly2
  8. Circle((0, 0), 1) → c
  9. Sequence(Rotate[poly1, i], i, 0, 6.283185307179586, (4 * π / n)) → liste5
  10. Translate(poly2, Vector[(0, 0, 1 + d)]) → poly2'
  11. Translate(Rotate[poly2, 1.5707963267948966, xAxis], Vector[(0, d + 1, 0)]) → poly3
  12. Translate(liste5, Vector[(0, 0, 1 + d)]) → liste5'
  13. Sequence(Rotate[poly3, i, zAxis], i, 1.5707963267948966, 4.71238898038469, 1.5707963267948966) → liste7
  14. Translate(Rotate[liste5, 1.5707963267948966, xAxis], Vector[(0, d + 1, 0)]) → liste8
  15. Sequence(Rotate[liste8, i, zAxis], i, 1.5707963267948966, 4.71238898038469, 1.5707963267948966) → liste9
  16. Sphere((0, 0, 0), 0.9) → b
  17. Translate(liste5, Vector[(0, 0, (-(1 + d)))]) → liste5'_1
  18. Polygon(G, H, F, I) → poly4, g, h, f, i
  19. Polygon(I, L, M, F) → poly5, i_1, l, m_1, f_1
  20. Polygon(G, J, L, I) → poly6, g_1, j, l_1, i_2
  21. Polygon(H, G, J, K) → poly7, h_1, g_2, j_1, k
  22. Polygon(F, H, K, M) → poly8, f_2, h_2, k_1, m_2
  23. Polygon(J, K, M, L) → poly9, j_2, k_2, m_3, l_2
  24. Polygon(R, W, V, U) → poly10, r, w, v, u