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Rotating Cube - JavaScript

Rotating Cube - JavaScript
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2018-01-30 00:17
Solid GeometryMatrixTransformation
This example demonstrates a rotating cube. Key mathematical concepts include matrix transformations and rotation. Using GeoGebra commands like Sequence, Join, and Polygon, the faces of the cube are constructed and its rotation is animated. Suitable for high school and above students learning solid geometry and transformations.

GeoGebra Commands & Parameters

  1. Sequence(Element[L_1, i] + (0, 0, h), i, 1, 4) → L_2
  2. Join({L_1, L_2}) → L_P
  3. Sequence(hom[Element[L_P, i]], i, 1, 8) → L_h
  4. Sequence((T * Element[L_h, i]), i, 1, 8) → L_T
  5. Sequence(((D * Element[L_T, i, 1, 1] / Element[L_T, i, 3, 1]), (D * Element[L_T, i, 2, 1] / Element[L_T, i, 3, 1])), i, 1, 8) → L_{Prj}
  6. Sequence(A - Element[PInPoly, i], i, 1, 6) → σList
  7. Sequence((Element[NList, i] * Element[σList, i]), i, 1, 6) → visibleL
  8. Join({Q_{10}, {Element[L_{Prj}, 1]}}) → Q_{11}
  9. Join({Q_{11}, {Element[L_{Prj}, 2]}}) → Q_{12}
  10. Join({Q_{12}, {Element[L_{Prj}, 3]}}) → Q_{13}
  11. Join({Q_{13}, {Element[L_{Prj}, 4]}}) → Q_{14}
  12. Polygon(Q_{14}) → P_1
  13. Join({Q_{20}, {Element[L_{Prj}, 5]}}) → Q_{21}
  14. Join({Q_{21}, {Element[L_{Prj}, 6]}}) → Q_{22}
  15. Join({Q_{22}, {Element[L_{Prj}, 7]}}) → Q_{23}
  16. Join({Q_{23}, {Element[L_{Prj}, 8]}}) → Q_{24}
  17. Polygon(Q_{24}) → P_2
  18. Join({Q_{30}, {Element[L_{Prj}, 1]}}) → Q_{31}
  19. Join({Q_{31}, {Element[L_{Prj}, 2]}}) → Q_{32}
  20. Join({Q_{32}, {Element[L_{Prj}, 6]}}) → Q_{33}
  21. Join({Q_{33}, {Element[L_{Prj}, 5]}}) → Q_{34}
  22. Polygon(Q_{34}) → P_3
  23. Join({Q_{40}, {Element[L_{Prj}, 2]}}) → Q_{41}
  24. Join({Q_{41}, {Element[L_{Prj}, 3]}}) → Q_{42}
  25. Join({Q_{42}, {Element[L_{Prj}, 7]}}) → Q_{43}
  26. Join({Q_{43}, {Element[L_{Prj}, 6]}}) → Q_{44}
  27. Polygon(Q_{44}) → P_4
  28. Join({Q_{50}, {Element[L_{Prj}, 3]}}) → Q_{51}
  29. Join({Q_{51}, {Element[L_{Prj}, 4]}}) → Q_{52}
  30. Join({Q_{52}, {Element[L_{Prj}, 8]}}) → Q_{53}
  31. Join({Q_{53}, {Element[L_{Prj}, 7]}}) → Q_{54}
  32. Polygon(Q_{54}) → P_5
  33. Join({Q_{60}, {Element[L_{Prj}, 1]}}) → Q_{61}
  34. Join({Q_{61}, {Element[L_{Prj}, 4]}}) → Q_{62}
  35. Join({Q_{62}, {Element[L_{Prj}, 8]}}) → Q_{63}
  36. Join({Q_{63}, {Element[L_{Prj}, 5]}}) → Q_{64}
  37. Polygon(Q_{64}) → P_6

AI Drawing Prompt Reference

Draw a rotating cube with six faces. First, create four points to represent the cube's vertices. Then, use matrix transformations to generate the rotated vertex coordinates. Next, draw six rectangular faces using these coordinates. Finally, connect these faces to form a rotating cube.
The prompt above was compiled from the original drawing commands and is for reference only.