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几何变换与平行四边形演示

几何变换与平行四边形演示
几何画板及绘图内容加载中，请稍等……
2016-06-15 06:20
解析几何变换几何作图
所属专题 My 3D Collection
①本范例演示了通过点a, b, c, d构造平行四边形及函数f的图像变换；②涉及的核心数学概念包括几何变换（平移）、平行四边形性质、函数图像变换；③作图要点：使用Segment命令绘制线段，Surface命令生成函数表面，对象包括f, a, b, c, d, e, g, h, i, j, k, l；④适合高中数学教学，用于理解几何变换与函数图像的关系。

GeoGebra 命令及参数

  1. Segment((0, 0, -1.5), (0, 0, 1.5)) → f
  2. Surface(((0.5 * cos(t)) * sin(f)), ((0.5 * sin(t)) * sin(f)), 1.5 + (0.2 * cos(f)), t, 0, (2 * π), f, 0, π) → a
  3. Surface(1 + (cos(t) * sin(f)), ((0.3 * sin(t)) * sin(f)), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → b
  4. Surface((cos(60°) * (1 + (cos(t) * sin(f)))) - (sin(60°) * ((0.3 * sin(t)) * sin(f))), (sin(60°) * (1 + (cos(t) * sin(f)))) + (cos(60°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → c
  5. Surface((cos(120°) * (1 + (cos(t) * sin(f)))) - (sin(120°) * ((0.3 * sin(t)) * sin(f))), (sin(120°) * (1 + (cos(t) * sin(f)))) + (cos(120°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → d
  6. Surface((-(1 + (cos(t) * sin(f)))) - (0 * ((0.3 * sin(t)) * sin(f))), (0 * (1 + (cos(t) * sin(f)))) + (-(((0.3 * sin(t)) * sin(f)))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → e
  7. Surface((cos(240°) * (1 + (cos(t) * sin(f)))) - (sin(240°) * ((0.3 * sin(t)) * sin(f))), (sin(240°) * (1 + (cos(t) * sin(f)))) + (cos(240°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → g
  8. Surface((cos(300°) * (1 + (cos(t) * sin(f)))) - (sin(300°) * ((0.3 * sin(t)) * sin(f))), (sin(300°) * (1 + (cos(t) * sin(f)))) + (cos(300°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → h
  9. Surface(1.2 + (1.2 * cos(f)), (sin(t) * sin(f)), -1 - (cos(t) * sin(f)), t, (5 / 6 * π), (7 / 6 * π), f, 0, π) → i
  10. Surface((cos(120°) * (1.2 + (1.2 * cos(f)))) - (sin(120°) * (sin(t) * sin(f))), (sin(120°) * (1.2 + (1.2 * cos(f)))) + (cos(120°) * (sin(t) * sin(f))), -1 - (cos(t) * sin(f)), t, (5 / 6 * π), (7 / 6 * π), f, 0, π) → j
  11. Surface((cos(240°) * (1.2 + (1.2 * cos(f)))) - (sin(240°) * (sin(t) * sin(f))), (sin(240°) * (1.2 + (1.2 * cos(f)))) + (cos(240°) * (sin(t) * sin(f))), -1 - (cos(t) * sin(f)), t, (5 / 6 * π), (7 / 6 * π), f, 0, π) → k
  12. Surface(((0.51 * cos(t)) * sin(f)), ((0.51 * sin(t)) * sin(f)), 1.5 + (0.21 * cos(f)), t, 0, (2 * π), f, (2 / 3 * π), π) → l

AI 绘图提示语参考

绘制一个平行四边形，使用点a、b、c、d作为顶点。首先画出点a、b、c、d，然后通过平移函数f的图像来展示几何变换。先画出f的图像，接着画出a、b、c、d、e、g、h、i、j、k、l，最后通过平移变换展示函数图像的变化。
以上提示语为根据原始绘图命令整理而来，仅供参考。