格兰维尔蛋参数曲线演示

几何画板及绘图内容加载中，请稍等……

2016-02-08 06:54

多边形函数参数方程

所属专题 surface 3D surface 3D

这个范例演示了如何通过参数方程绘制复杂的曲线，涉及的核心数学概念包括参数曲线、多边形、指数函数、线性函数和线段。作图要点使用了GeoGebra的If和Surface命令，以及对象e, m, a, b, r, d, m3, m2, m7, m6, m5, m4, U, oe2, oe3, oe4, oe5, oe6, oe7, oe1, op。适合高中及以上学生学习和探索参数方程的应用。

GeoGebra 命令及参数

If(m < 1, 0, If[m < 2, (e * (m - 1)), e]) → m3
If(m < 1, (e * m), e) → m2
If(m < 5, 0, If[m < 6, (e * (m - 5)), e]) → m7
If(m < 4, 0, If[m < 5, (e * (m - 4)), e]) → m6
If(m < 3, 0, If[m < 4, (e * (m - 3)), e]) → m5
If(m < 2, 0, If[m < 3, (e * (m - 2)), e]) → m4
Surface((((a * (r + d)) * sin(t)) * cos(u) / (b + ((r + d) * cos(t)))), (((a * (r + d)) * sin(t)) * sin(u) / (b + ((r + d) * cos(t)))), ((r + d) * cos(t)), t, m7, π, u, (-π), U) → oe2
Surface((((a * (r + (2 * d))) * sin(t)) * cos(u) / (b + ((r + (2 * d)) * cos(t)))), (((a * (r + (2 * d))) * sin(t)) * sin(u) / (b + ((r + (2 * d)) * cos(t)))), ((r + (2 * d)) * cos(t)), t, m6, π, u, (-π), U) → oe3
Surface((((a * (r + (3 * d))) * sin(t)) * cos(u) / (b + ((r + (3 * d)) * cos(t)))), (((a * (r + (3 * d))) * sin(t)) * sin(u) / (b + ((r + (3 * d)) * cos(t)))), ((r + (3 * d)) * cos(t)), t, m5, π, u, (-π), U) → oe4
Surface((((a * (r + (4 * d))) * sin(t)) * cos(u) / (b + ((r + (4 * d)) * cos(t)))), (((a * (r + (4 * d))) * sin(t)) * sin(u) / (b + ((r + (4 * d)) * cos(t)))), ((r + (4 * d)) * cos(t)), t, m4, π, u, (-π), U) → oe5
Surface((((a * (r + (5 * d))) * sin(t)) * cos(u) / (b + ((r + (5 * d)) * cos(t)))), (((a * (r + (5 * d))) * sin(t)) * sin(u) / (b + ((r + (5 * d)) * cos(t)))), ((r + (5 * d)) * cos(t)), t, m3, π, u, (-π), U) → oe6
Surface((((a * (r + (6 * d))) * sin(t)) * cos(u) / (b + ((r + (6 * d)) * cos(t)))), (((a * (r + (6 * d))) * sin(t)) * sin(u) / (b + ((r + (6 * d)) * cos(t)))), ((r + (6 * d)) * cos(t)), t, m2, π, u, (-π), U) → oe7
Surface((((a * r) * sin(t)) * cos(u) / (b + (r * cos(t)))), (((a * r) * sin(t)) * sin(u) / (b + (r * cos(t)))), (r * cos(t)), t, 0, π, u, (-π), π) → oe1