使用python和mayavi创建3D streamplot

Question

目前很容易使用python和matplotlib生成2D streamplot,因为最近由Tom Flannaghan和Tony Yu将matamplot插入matplotlib.

虽然可以使用matplotlib生成某些类型的3D绘图,但目前不支持3D streamplots.然而,python绘图程序mayavi(提供基于vtk的绘图的python接口)能够使用其flow()函数的3D streamplots .

我已经创建了一个简单的python模块来对2D和3D中的数据进行流绘图,在3D数据集中没有Z斜率(所有dZ = 0),以演示我在mayavi与matplotlib有效匹配数据时所面临的绘图挑战在xy平面上.注释的代码和结果图如下所示:

import numpy, matplotlib, mayavi, matplotlib.pyplot, mayavi.mlab
#for now, let's produce artificial streamline data sets for 2D & 3D cases where x and y change by +1 at each point, while Z changes by 0 at each point:

#2D data first:
x = numpy.ones((10,10))
y = numpy.ones((10,10))
#and a corresponding meshgrid:
Y,X = numpy.mgrid[-10:10:10j,-10:10:10j]

#now 3D data with Z = 0 (i.e., I want to be able to produce a matching streamplot plane in mayavi, which is normally used for 3D):
xx = numpy.ones((10,10,10))
yy = numpy.ones((10,10,10))
zz = numpy.zeros((10,10,10))
#and a corresponding meshgrid:
ZZ,YY,XX = numpy.mgrid[-10:10:10j,-10:10:10j,-10:10:10j]

#plot the 2D streamplot data with matplotlib:
fig = matplotlib.pyplot.figure()
ax = fig.add_subplot(111,aspect='equal')
speed = numpy.sqrt(x*x + y*y)
ax.streamplot(X, Y, x, y, color=x, linewidth=2, cmap=matplotlib.pyplot.cm.autumn,arrowsize=3)
fig.savefig('test_streamplot_2D.png',dpi=300)

#there's no streamplot 3D available in matplotlib, so try to see how mayavi behaves with a similar 3D data set:
fig = mayavi.mlab.figure(bgcolor=(1.0,1.0,1.0),size=(800,800),fgcolor=(0, 0, 0))
st = mayavi.mlab.flow(XX,YY,ZZ,xx,yy,zz,line_width=4,seedtype='sphere',integration_direction='forward') #sphere is the default seed type
mayavi.mlab.axes(extent = [-10.0,10.0,-10.0,10.0,-1.0,1.0]) #set plot bounds
fig.scene.z_plus_view() #adjust the view for a perspective along z (xy plane flat)
mayavi.mlab.savefig('test_streamplot_3D_attempt_1.png')

#now start to modify the mayavi code to see if I can 'seed in' more streamlines (default only produces a single short streamline, albeit of the correct slope)
#attempt 2 uses a line seed / widget over the specified bounds (points 1 and 2):
fig = mayavi.mlab.figure(bgcolor=(1.0,1.0,1.0),size=(800,800),fgcolor=(0, 0, 0))
st = mayavi.mlab.flow(XX,YY,ZZ,xx,yy,zz,line_width=4,seedtype='line',integration_direction='forward') #line instead of sphere
st.seed.widget.point1 = [0,-10,0]
st.seed.widget.point2 = [0,10,0] #so seed line should go up along y axis
st.seed.widget.resolution = 25 #seems to be the number of seeds points along the seed line
mayavi.mlab.axes(extent = [-10.0,10.0,-10.0,10.0,-1.0,1.0]) #set plot bounds
fig.scene.z_plus_view() #adjust the view for a perspective along z (xy plane flat)
mayavi.mlab.savefig('test_streamplot_3D_attempt_2.png')

#attempt 3 will try to seed a diagonal line across the plot to produce streamlines that cover the full plot:
#would need to use 'both' for integration_direction if I could get the diagonal seed line to work
fig = mayavi.mlab.figure(bgcolor=(1.0,1.0,1.0),size=(800,800),fgcolor=(0, 0, 0)) 
st = mayavi.mlab.flow(XX,YY,ZZ,xx,yy,zz,line_width=4,seedtype='line',integration_direction='forward') 
st.seed.widget.point1 = [-10,10,0] #start seed line at top left corner of plot
st.seed.widget.point2 = [10,-10,0] #end seed line at bottom right corner of plot 
#this fails to produce a diagonal seed line though
st.seed.widget.resolution = 25 #seems to be the number of seeds points along the seed line
mayavi.mlab.axes(extent = [-10.0,10.0,-10.0,10.0,-1.0,1.0]) #set plot bounds
fig.scene.z_plus_view() #adjust the view for a perspective along z (xy plane flat)
mayavi.mlab.savefig('test_streamplot_3D_attempt_3.png')

2D matplotlib结果(注意斜率1的流线与dx和dy数组完全匹配,所有dl和dy数组都填充了单位值): 3D mayavi结果(尝试1; 请注意,此处存在的单个流线的斜率是正确的,但流线的长度和数量显然与2D matplotlib示例完全不同): 3D mayavi结果(尝试2; 注意我使用具有足够高分辨率的线种子产生了更多适当斜率的流线,但也注意到代码中指定的黑色种子线的起始和结束x坐标'与情节匹配) 最后,尝试#3(令人困惑)产生与#2完全相同的图,尽管规定了不同的种子/小部件点.所以,问题是:我怎样才能更好地控制种子线的位置以使其成为对角线？更广泛地说,我希望能够提供任意数量的种子点以获得更一般的流图3D(非平面)问题,但是用线来解决前一个特定情况应该让我开始.

我在处理这个问题时发现了一些其他有用的资源,这些资源并没有完全解决我的问题:

1. matplotlib streamplot共同作者Tom Flannaghan 关于该主题的博客文章
2. 一个例子,其中种子的一个自定义的阵列用于与Mayavi的流线的一个子类(其又,所使用的流量()),但不幸的是与实现细节不足重现.
3. 示例,包括注释的源代码,用于使用mayavi来产生磁场线的2D流动图.
4. 3D中的源代码的类似示例,但仍不足以解决我的绘图问题:
5. 由mayavi标准文档中提供的示例代码生成的flow()图(在流线后面可以看到球形种子窗口小部件).

Answer 1

似乎问题是流线种子窗口小部件的clamp_to_bounds属性的默认值设置为True.您必须将此设置为False才能实际移动窗口小部件.

st.seed.widget.clamp_to_bounds = False

将此添加到代码后,最终结果如下所示:

你可能已经熟悉了以前探索Mayavi的这种方法,但是有可能解释得太多,我会提到这个:

我发现这个选项的方式,以及我通常如何在Mayavi中找到这些模糊的属性,是通过启用pylab启动IPython的脚本.在Ubuntu上,terminal命令如下所示:

ipython --pylab=qt

启动IPython后,我使用%run magic命令运行脚本:

%run streamlines.py

绘制完成后,我现在可以访问Mayavi窗口,可以通过单击Mayavi图标查看Mayavi管道的内部:

在管道中,您将找到Streamline对象,如果单击它然后选择Seed,您将找到"Clamp to bounds"复选框.(抱歉屏幕截图中的颜色组合很糟糕 - Mayavi最近开始使用黑暗主题......)

要查看其实际功能,您可以点击录制按钮 打开一个窗口,显示相当于更改设置的代码:

在那里你可以看到clamp_to_bounds属性,并且可以将它添加到你的脚本中.

祝你好运!