目前很容易使用

python和matplotlib生成2D streamplot,因为最近

streamplot由Tom Flannaghan和Tony Yu合并到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()功能的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种子线的开始和结束x坐标不符合情节)

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：

> matplotlib streamplot共同作者Tom Flannaghan关于这个主题的blog post

> example,其中自定义种子数组与mayavi Streamline的子类一起使用(反过来,由flow()使用),但遗憾的是实现细节不足以重现.

>使用mayavi生成2D streamplots of magnetic field lines的示例,包括注释的源代码.

> Similar examples with source in 3D,但仍不足以解决我的密谋问题：

> mayavi标准文档中提供的flow()plot resulting from the example code(在流线后面可以看到球形种子窗口小部件).