旋转立方体 - JavaScript

旋转立方体 - JavaScript
几何画板及绘图内容加载中,请稍等……
2018-01-30 00:17
该范例演示了一个立方体的旋转动画。核心数学概念包括矩阵变换和旋转。通过使用GeoGebra命令Sequence, Join, Polygon等,可以构造出立方体的各个面,并实现其旋转效果。适合高中及以上学生学习立体几何和变换。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个旋转的正方体,包含六个面。首先创建四个点,表示正方体的顶点,然后通过矩阵变换生成旋转后的顶点坐标,接着使用这些坐标绘制六个矩形面,最后将这些矩形面连接起来形成一个旋转的正方体。
以上提示语为根据原始绘图命令整理而来,仅供参考。