蝴蝶曲面

几何画板及绘图内容加载中，请稍等……

2015-03-24 04:48

所属专题 surface 3D surface 3D

①本范例演示了一个彩色蝴蝶曲面，通过叠加三个相同的表面但进行变换，呈现出清晰的视觉效果；②涉及的核心数学概念包括三维曲面、颜色映射、变换几何；③作图要点使用了Surface（曲面）、CurveCartesian（笛卡尔曲线）等命令，涉及参数Umin, UmaxB, c, e, VmaxR, UmaxR, VmaxB, VmaxY, UmaxY, Umax, Vmax, g, d, b, f等对象；④适合高中及以上学生学习和探索立体几何与参数化曲面的特性。

GeoGebra 命令及参数

Surface(((cos(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), ((sin(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), (cos(u) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), u, Umin, UmaxR, v, (-VmaxR), VmaxR) → g
CurveCartesian((sin(t) * ((e * ℯ^(cos(t))) - (c * cos((4 * t))) - sin(t / 12)^(2))), (cos(t) * ((e * ℯ^(cos(t))) - (c * cos((4 * t))) - sin(t / 12)^(2))), t, Umin, Max[{Umax, UmaxR, UmaxB, UmaxY}]) → d
Surface(((cos(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), ((sin(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), (cos(u) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), u, Umin, UmaxB, v, (-VmaxB), VmaxB) → b
Surface(((cos(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), ((sin(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), (cos(u) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), u, Umin, UmaxY, v, (-VmaxY), VmaxY) → f