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两曲面交线：圆柱-余弦曲面

两曲面交线：圆柱-余弦曲面
几何画板及绘图内容加载中，请稍等……
2016-08-29 18:17
三角函数解析几何参数方程
所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
本范例展示了在区间[-π, π]内，圆柱面与余弦曲面的交线。核心数学概念包括曲面交线、三角函数。通过GeoGebra命令Sequence、Textfield、InputBox等构造交线，适合高中数学教学。

GeoGebra 命令及参数

  1. Textfield(x0) → InputBox1
  2. Textfield(y0) → InputBox2
  3. Sequence((i * acos((-cos(x)) - cos(y))), i, -1, 1, 2) → l_f
  4. Textfield(z0) → InputBox3
  5. Sequence(CurveCartesian[t, (i * acos((-cos(f1(t))) - cos(t))), f1(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1
  6. Sequence(CurveCartesian[t, (i * acos((-cos(f2(t))) - cos(t))), f2(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2
  7. Sequence(CurveCartesian[x0, (i * acos((-cos(f1(t))) - cos(t))), f1(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1_{x}
  8. Sequence(CurveCartesian[t, y0, f1(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1_{y}
  9. Sequence(CurveCartesian[t, (i * acos((-cos(f1(t))) - cos(t))), z0, t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1_{z}
  10. Sequence(CurveCartesian[x0, (i * acos((-cos(f2(t))) - cos(t))), f2(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2_{x}
  11. Sequence(CurveCartesian[t, y0, f2(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2_{y}
  12. Sequence(CurveCartesian[t, (i * acos((-cos(f2(t))) - cos(t))), z0, t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2_{z}

AI 绘图提示语参考

绘制一个圆柱体与余弦曲面的交集，交集范围为[-π, π]。首先输入圆柱体的x轴、y轴和z轴的偏移量，然后根据这些偏移量绘制两个余弦曲面，每个曲面有正负两个分支，最后绘制每个曲面在x轴、y轴和z轴上的投影。
以上提示语为根据原始绘图命令整理而来，仅供参考。