圆锥曲线可视化
Posted on 06 Jun 2015 Mathematica 添加评论
学习圆锥曲线的时候一直感觉课本上那个图很好看，所以也来画画看。
接着上面的文章，先画没有圆柱的：
p = ContourPlot3D[x - z /30, {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
ContourStyle -> Opacity[0.5], PlotPoints -> 20,
MeshFunctions -> Function[{x, y, z}, y^2 + x^2 - z^2],
MeshStyle -> {Tube[0.03]}, Mesh -> 0,
ColorFunction -> CreateColorFunction[Paired, 4],
BoundaryStyle -> None, Boxed -> False]
这次加圆柱反而比较困难，因为这次我想把交贯线画出来：
ContourPlot3D[{x - z/3 + 1/2 , y^2 + x^2 - z^2 == 0}, {x, -2,
2}, {y, -2, 2}, {z, -2, 2}, ContourStyle -> Opacity[0.5],
PlotPoints -> 20, Mesh -> None,
ColorFunction -> CreateColorFunction[Paired, 4],
BoundaryStyle -> {1 -> None,
2 -> None, {1, 2} -> { {Green, Tube[.03]} } }, Boxed -> False]
其实最好的办法不是像上面那样话。可以这样来，而且好处是你可以调节圆锥的参数使得两个的配比更为合适，这里仅仅调整了透明度。
cone = ContourPlot3D[
y^2 + x^2 - z^2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
ContourStyle -> Opacity[0.2], PlotPoints -> 20,
ColorFunction -> CreateColorFunction[Paired, 4], Mesh -> None,
BoundaryStyle -> None, Boxed -> False];
Show[p, cone]
