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参数曲面与几何作图

参数曲面与几何作图
几何画板及绘图内容加载中，请稍等……
2017-04-03 16:30
解析几何立体几何参数方程
所属专题 surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
本范例展示了如何通过两个函数构造参数曲面。首先，一个函数作为基础，另一个函数作为高度。通过曲线和曲面的构造，可以直观地理解参数方程和立体几何的概念。使用了CurveCartesian, Intersect, Surface, Segment, Vector等GeoGebra命令。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. CurveCartesian(t, f(t), g(t), t, -5, 5) → a
  2. CurveCartesian(t, g(t), f(t), t, -5, 5) → b
  3. Intersect(f, g, (-0.8241323136805904, 0.679194070452523)) → A
  4. Intersect(g, f, (0.8241323126131453, 0.679194067953118)) → B
  5. Surface(t, (u * g(t)) + ((1 - u) * f(t)), f(t), t, x(A), x(B), u, 0, 1) → c
  6. Surface(t, (u * g(t)) + ((1 - u) * f(t)), 0, t, x(A), x(B), u, 0, 1) → d
  7. Surface(t, (u * g(t)) + ((1 - u) * f(t)), g(t), t, x(A), x(B), u, 0, 1) → e
  8. Surface(t, g(t), (u * f(t)), t, x(A), x(B), u, 0, 1) → i
  9. Surface(t, f(t), (u * g(t)), t, x(A), x(B), u, 0, 1) → h
  10. Surface(t, f(t), (u * f(t)), t, x(A), x(B), u, 0, 1) → j
  11. Surface(t, g(t), (u * g(t)), t, x(A), x(B), u, 0, 1) → k
  12. Segment(A', B') → l
  13. Vector(A', B') → u
  14. CurveCartesian(x(A) + (t * x(u)), y(A), f(x(A)), t, -5, 5) → m
  15. Textfield(f) → CampEntradaSortida1
  16. Textfield(g) → CampEntradaSortida2
  17. Surface(t, (u * y(A)) + ((1 - u) * g(t)), (u * f(x(A))) + ((1 - u) * f(t)), t, x(A), x(B), u, 0, 1) → n
  18. Surface(t, (u * y(A)) + ((1 - u) * f(t)), (u * f(x(A))) + ((1 - u) * g(t)), t, x(A), x(B), u, 0, 1) → o
  19. Segment(A', A) → p
  20. Segment(B', B) → q