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双曲立方体

双曲立方体
几何画板及绘图内容加载中，请稍等……
2023-03-15 19:39
解析几何立体几何几何作图
所属专题 geometriadinamica.es
这个范例展示了双曲立方体的几何构造。它涉及双曲线几何和立体几何的核心概念。通过使用GeoGebra命令如Segment, Point, OrthogonalLine等，可以构建出双曲立方体的各个面和边。适合高中或大学的立体几何课程使用。

GeoGebra 命令及参数

  1. Segment(Q3, Q4) → p2
  2. Point(p2) → P3
  3. Segment(P3, Q4) → p4
  4. Point(p4) → P4
  5. Segment(Q5, Q6) → p5
  6. Point(p5) → P5
  7. Segment(Q1, Q2) → p1
  8. Point(p1) → P1
  9. Segment(P1, Q2) → p3
  10. Point(p3) → P2
  11. OrthogonalLine(C, xAxis) → zz2
  12. Circle(C, 0.62) → zz0
  13. Intersect(zz0, zz2, 1) → ZZ4
  14. Intersect(zz0, zz2, 2) → ZZ3
  15. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  16. Point(zElipse2) → Z
  17. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  18. Angle(ZZ8, C, Z) → zAngInc
  19. OrthogonalLine(C, yAxis) → zz1
  20. Intersect(zz0, zz1, 2) → ZZ2
  21. Intersect(zz0, zz1, 1) → ZZ1
  22. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  23. Point(zElipse1) → XY
  24. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  25. Angle(ZZ6, C, XY) → zAngRot
  26. Segment(ZZ5, ZZ6) → zz4
  27. Segment(ZZ7, ZZ8) → zz3
  28. Intersect(zElipse2, zElipse1, 1) → zPunto1
  29. Intersect(zElipse2, zElipse1, 4) → zPunto2
  30. Segment(zPunto1, zPunto2) → zSeg2
  31. CurveCartesian((r / 1.2 * (((((cos(v))^(3) + (sin(v))^(3)) * ((cos(α))^(3) + (sin(α))^(3))) * sin(zAngRot)) + ((((-(cos(v))^(3)) + (sin(v))^(3)) * ((cos(α))^(3) + (sin(α))^(3))) * cos(zAngRot)))), (r / 1.2 * (((((-((cos(v))^(3) + (sin(v))^(3))) * ((cos(α))^(3) + (sin(α))^(3))) * cos(zAngRot)) * sin(zAngInc)) + (((((-(cos(v))^(3)) + (sin(v))^(3)) * ((cos(α))^(3) + (sin(α))^(3))) * sin(zAngRot)) * sin(zAngInc)) + (((-(cos(α))^(3)) + (sin(α))^(3)) * cos(zAngInc)))), v, v1, v2) → curva2
  32. CurveCartesian((r / 1.2 * (((-((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) + (((cos(u))^(3) + (sin(u))^(3)) * cos(zAngRot)))), (r / 1.2 * (((((cos(u))^(3) + (sin(u))^(3)) * cos(zAngRot)) * sin(zAngInc)) + ((((cos(u))^(3) + (sin(u))^(3)) * sin(zAngRot)) * sin(zAngInc)) + (((-(cos(u))^(3)) + (sin(u))^(3)) * cos(zAngInc)))), u, u1, u2) → curva1
  33. CurveCartesian((r / 1.2 * (((((cos(β))^(3) + (sin(β))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) + ((((-(cos(β))^(3)) + (sin(β))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * cos(zAngRot)))), (r / 1.2 * (((((-((cos(β))^(3) + (sin(β))^(3))) * ((cos(u))^(3) + (sin(u))^(3))) * cos(zAngRot)) * sin(zAngInc)) + (((((-(cos(β))^(3)) + (sin(β))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) * sin(zAngInc)) + (((-(cos(u))^(3)) + (sin(u))^(3)) * cos(zAngInc)))), u, u1, u2) → a1
  34. Sequence(CurveCartesian[(r / 1.2 * (((((cos(v))^(3) + (sin(v))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) + ((((-(cos(v))^(3)) + (sin(v))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * cos(zAngRot)))), (r / 1.2 * (((((-((cos(v))^(3) + (sin(v))^(3))) * ((cos(u))^(3) + (sin(u))^(3))) * cos(zAngRot)) * sin(zAngInc)) + (((((-(cos(v))^(3)) + (sin(v))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) * sin(zAngInc)) + (((-(cos(u))^(3)) + (sin(u))^(3)) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list3
  35. Sequence(CurveCartesian[(r / 1.2 * (((((cos(v))^(3) + (sin(v))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) + ((((-(cos(v))^(3)) + (sin(v))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * cos(zAngRot)))), (r / 1.2 * (((((-((cos(v))^(3) + (sin(v))^(3))) * ((cos(u))^(3) + (sin(u))^(3))) * cos(zAngRot)) * sin(zAngInc)) + (((((-(cos(v))^(3)) + (sin(v))^(3)) * ((cos(u))^(3) + (sin(u))^(3))) * sin(zAngRot)) * sin(zAngInc)) + (((-(cos(u))^(3)) + (sin(u))^(3)) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list1

AI 绘图提示语参考

绘制一个双曲立方体的三维几何构造图。先建立坐标轴和中心点，在中心点处作两个相互垂直的椭圆，分别代表两个旋转平面。在每个椭圆上取点，并连接这些点形成立方体的棱和面。通过旋转和投影，生成一系列曲线网格，覆盖立方体的表面，表现出双曲几何的弯曲特性。整体图形由中心点、两个椭圆、若干条棱边以及密集的曲线网格构成，呈现对称且扭曲的立体形态。
以上提示语为根据原始绘图命令整理而来，仅供参考。