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链条扭转

链条扭转
几何画板及绘图内容加载中，请稍等……
2016-10-23 21:30
微积分变换几何作图
这个范例演示了链条的扭转现象。核心数学概念包括几何作图和变换。使用了Surface、对象r、R、k、d、torsion、rotation等GeoGebra命令。适合用于高中或大学的几何和微积分课程。

GeoGebra 命令及参数

  1. Surface((((R + (r * cos(v))) * sin(u)) * cos(rotation + (π / 2 * (1 - torsion + (torsion * sin(u / 2)))))) - ((sin(rotation + (π / 2 * (1 - torsion + (torsion * sin(u / 2))))) * r) * sin(v)), d + (((k * R) + (r * cos(v))) * cos(u)), (((R + (r * cos(v))) * sin(u)) * sin(rotation + (π / 2 * (1 - torsion + (torsion * sin(u / 2)))))) + ((cos(rotation + (π / 2 * (1 - torsion + (torsion * sin(u / 2))))) * r) * sin(v)), u, 0, (2 * π), v, (-π), π) → a
  2. Surface((((R + (r * cos(v))) * sin(u)) * cos(rotation + ((π / 2 * torsion) * (2 + sin(u / 2))))) - ((sin(rotation + ((π / 2 * torsion) * (2 + sin(u / 2)))) * r) * sin(v)), (-2 * d) + (((k * R) + (r * cos(v))) * cos(u)), (((R + (r * cos(v))) * sin(u)) * sin(rotation + ((π / 2 * torsion) * (2 + sin(u / 2))))) + ((cos(rotation + ((π / 2 * torsion) * (2 + sin(u / 2)))) * r) * sin(v)), u, 0, (2 * π), v, (-π), π) → aa
  3. Surface((((R + (r * cos(v))) * sin(u)) * cos(rotation + ((π / 2 * torsion) * (-2 + sin(u / 2))))) - ((sin(rotation + ((π / 2 * torsion) * (-2 + sin(u / 2)))) * r) * sin(v)), (2 * d) + (((k * R) + (r * cos(v))) * cos(u)), (((R + (r * cos(v))) * sin(u)) * sin(rotation + ((π / 2 * torsion) * (-2 + sin(u / 2))))) + ((cos(rotation + ((π / 2 * torsion) * (-2 + sin(u / 2)))) * r) * sin(v)), u, 0, (2 * π), v, (-π), π) → bb
  4. Surface((((R + (r * cos(v))) * sin(u)) * cos(rotation + ((π / 2 * torsion) * sin(u / 2)))) - ((sin(rotation + ((π / 2 * torsion) * sin(u / 2))) * r) * sin(v)), (((k * R) + (r * cos(v))) * cos(u)), (((R + (r * cos(v))) * sin(u)) * sin(rotation + ((π / 2 * torsion) * sin(u / 2)))) + ((cos(rotation + ((π / 2 * torsion) * sin(u / 2))) * r) * sin(v)), u, 0, (2 * π), v, (-π), π) → c
  5. Surface((((R + (r * cos(v))) * sin(u)) * cos((-rotation) + (π / 2 * (1 - torsion + (torsion * sin(((-u)) / 2)))))) - ((sin((-rotation) + (π / 2 * (1 - torsion + (torsion * sin(((-u)) / 2))))) * r) * sin(v)), (-d) + (((k * R) + (r * cos(v))) * cos(u)), (-((((R + (r * cos(v))) * sin(u)) * sin((-rotation) + (π / 2 * (1 - torsion + (torsion * sin(((-u)) / 2)))))) + ((cos((-rotation) + (π / 2 * (1 - torsion + (torsion * sin(((-u)) / 2))))) * r) * sin(v)))), u, 0, (2 * π), v, (-π), π) → b

AI 绘图提示语参考

绘制一个链状扭曲图形，包含四个曲面。首先绘制一个扭曲的链状表面，使用参数R、r、k、d、torsion和rotation。接着绘制三个对称的扭曲表面，分别位于d、-2d和2d处，使用相同的参数。最后绘制一个旋转扭曲的表面，使用参数torsion和u/v的正弦函数。
以上提示语为根据原始绘图命令整理而来，仅供参考。