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苹果形状的参数曲线与曲面

苹果形状的参数曲线与曲面
几何画板及绘图内容加载中，请稍等……
2016-01-16 20:38
立体几何参数方程几何作图
①这个范例通过参数方程演示了如何绘制一个苹果形状的曲线和曲面；②涉及的核心数学概念包括参数曲线、曲面、正交线、交点、镜像、圆弧、距离、角度等；③作图要点使用了GeoGebra命令如CurveCartesian, Tangent, OrthogonalLine, Intersect, Mirror, CircleArc, Distance, Angle, Surface等；④适合高中及以上学生学习和理解参数方程在几何绘图中的应用。

GeoGebra 命令及参数

  1. CurveCartesian((-(p_1 + (3.8 * cos(v)))), (((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (p_2 * sin(v)), v, b_1, b_2) → c_3
  2. Tangent(B, c_3) → tg
  3. OrthogonalLine(B, tg) → lot
  4. Intersect(lot, yAxis) → C
  5. Mirror(B, yAxis) → B'
  6. CircleArc(C, B', B) → c
  7. Distance(C, B) → r
  8. Angle(lot, yAxis) → wi
  9. Surface(((r * cos(u)) * sin(v)), ((r * sin(u)) * sin(v)), z(M) - (r * cos(v)), u, π, π + a, v, π, (2 * π) - wi) → e
  10. CurveCartesian((r * sin(v)), ((r * 0) * sin(v)), z(M) - (r * cos(v)), v, π, (2 * π) - wi) → k_1
  11. CurveCartesian(((r * (-1)) * sin(v)), ((r * 0) * sin(v)), z(M) - (r * cos(v)), v, π, (2 * π) - wi) → k_2
  12. Surface((cos(u) * (p_1 + (3.8 * cos(v)))), (sin(u) * (p_1 + (3.8 * cos(v)))), (((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (p_2 * sin(v)), u, 0, a, v, b_1, b_2) → apple
  13. CurveCartesian((-(p_1 + (3.8 * cos(v)))), (0 * (p_1 + (3.8 * cos(v)))), (((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (p_2 * sin(v)), v, b_1, b_2) → c_1
  14. CurveCartesian(p_1 + (3.8 * cos(v)), (0 * (p_1 + (3.8 * cos(v)))), (((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (p_2 * sin(v)), v, b_1, b_2) → c_2
  15. CurveCartesian(p_1 + (3.8 * cos(v)), (((cos(v) + sin(v) - 1) * (1 + sin(v))) * log(1 - (π * v / 10))) + (p_2 * sin(v)), v, b_1, b_2) → c_4