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绘制曲面

绘制曲面
几何画板及绘图内容加载中，请稍等……
2016-08-31 08:24
函数解析几何立体几何导数最值优化
①本范例演示如何使用 GeoGebra 绘制三维空间中的曲面图形；②涉及的核心数学概念包括曲面、优化问题、解析几何、二次方程、切线等；③作图要点——从下方『构造摘要』提炼用到了 Textfield, CurveCartesian, Intersect, Point, Ray, Segment 等命令/对象；④适合高中及以上学生及数学爱好者学习三维图形绘制与相关数学概念。

GeoGebra 命令及参数

  1. Textfield(x_0) → InputBox1
  2. Textfield(y_0) → InputBox2
  3. CurveCartesian(x_0, t, f(x_0, t), t, -10, 10) → Z_y
  4. CurveCartesian(t, y_0, f(t, y_0), t, -10, 10) → Z_x
  5. Textfield(f) → InputBox3
  6. Intersect(yAxis, xAxis) → Origin
  7. Point(xAxis) → x_{axis}Point
  8. Ray(Origin, x_{axis}Point) → x_{axis}
  9. Point(yAxis) → y_{axis}Point
  10. Ray(Origin, y_{axis}Point) → y_{axis}
  11. Point(zAxis) → z_{axis}Point
  12. Ray(Origin, z_{axis}Point) → z_{axis}
  13. Segment(Y_02D, B) → m
  14. Segment(X_02D, A) → n
  15. Segment(C, Intersection) → g
  16. Segment(C, X_03D) → h
  17. Segment(C, Y_03D) → i
  18. Segment(D, Y_03D) → j
  19. Segment(D, X_03D) → k