Question

目前使用python和matplotlib制作2D streamplot非常容易，因为streamplot最近由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()函数进行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streamplot，在3D数据集中没有Z-slope（所有dZ = 0），以展示我与mayavi对比matplotlib所面临的绘图挑战有效地匹配xy平面中的数据。评论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）： 2D matplotlib streamplot 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）： enter image description here 3D mayavi结果（尝试2; 请注意，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，但也注意到黑色种子线的开始和结束x坐标代码与情节不匹配）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：如何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，但是解决前一个特定情况的线应该让我开始。