mlab: scripting for 3D plotting

Section summary

This section describes the mab API, for use of Mayavi as a simple plotting in scripts or interactive sessions. This is the main entry point for people interested in doing 3D plotting à la Matlab or IDL in Python. If you are interested in a list of all the functions exposed in mlab, see the MLab reference.

The enthought.mayavi.mlab module, that we call mlab, provides an easy way to visualize data in a script or from an interactive prompt with one-liners as done in the matplotlib pylab interface but with an emphasis on 3D visualization using Mayavi2. This allows users to perform quick 3D visualization while being able to use Mayavi’s powerful features.

Mayavi’s mlab is designed to be used in a manner well-suited to scripting and does not present a fully object-oriented API. It is can be used interactively with IPython_.

Warning

When using IPython with mlab, as in the following examples, IPython must be invoked with the -wthread command line option like so:

$ ipython -wthread

If you are using the Enthought Python Distribution, or the latest Python(x,y) distribution, the Pylab menu entry will start ipython with the right switch. In older release of Python(x,y) you need to start “Interactive Console (wxPython)”.

For more details on using mlab and running scripts, read the section Running mlab scripts

In this section, we first introduce simple plotting functions, to create 3D objects as representations of numpy arrays. Then we explain how properties such as color or glyph size can be modified or used to represent data, we show how the visualization created throught mlab can be modified interactively with dialogs, we show how scripts and animations can be ran. Finally, we expose a more advanced use of mlab in which full visualization pipeline are built in scripts, and we give some detailled examples of applying these tools to visualizing volumetric scalar and vector data.

A demo

To get you started, here is a pretty example showing a spherical harmonic as a surface:

# Create the data.
from numpy import pi, sin, cos, mgrid
dphi, dtheta = pi/250.0, pi/250.0
[phi,theta] = mgrid[0:pi+dphi*1.5:dphi,0:2*pi+dtheta*1.5:dtheta]
m0 = 4; m1 = 3; m2 = 2; m3 = 3; m4 = 6; m5 = 2; m6 = 6; m7 = 4;
r = sin(m0*phi)**m1 + cos(m2*phi)**m3 + sin(m4*theta)**m5 + cos(m6*theta)**m7
x = r*sin(phi)*cos(theta)
y = r*cos(phi)
z = r*sin(phi)*sin(theta)

# View it.
from enthought.mayavi import mlab
s = mlab.mesh(x, y, z)
mlab.show()

Bulk of the code in the above example is to create the data. One line suffices to visualize it. This produces the following visualization:

The visualization is created by the single function mesh() in the above.

Several examples of this kind are provided with mlab (see test_contour3d, test_points3d, test_plot3d_anim etc.). The above demo is available as test_mesh. Under IPython these may be found by tab completing on mlab.test. You can also inspect the source in IPython via the handy mlab.test_contour3d??.

3D Plotting functions for numpy arrays

Visualization can be created in mlab by a set of functions operating on numpy arrays.

The mlab plotting functions take numpy arrays as input, describing the x, y, and z coordinates of the data. They build full-blown visualizations: they create the data source, filters if necessary, and add the visualization modules. Their behavior, and thus the visualization created, can be fine-tuned through keyword arguments, similarly to pylab. In addition, they all return the visualization module created, thus visualization can also be modified by changing the attributes of this module.

Note

In this section, we only list the different functions. Each function is described in details in the MLab reference, at the end of the user guide, with figures and examples. Please follow the links.

0D and 1D data

	points3d() Plots glyphs (like points) at the position of the supplied data, described by x, y, z numpy arrays of the same shape.
	plot3d() Plots line between the supplied data, described by x, y, z 1D numpy arrays of the same length.

2D data

	imshow() View a 2D array as an image.
	surf() View a 2D array as a carpet plot, with the z axis representation through elevation the value of the array points.
	contour_surf() View a 2D array as line contours, elevated according to the value of the array points.
	mesh() Plot a surface described by three 2D arrays, x, y, z giving the coordinnates of the data points as a grid. Unlike surf(), the surface is defined by its x, y and z coordinates with no privileged direction. More complex surfaces can be created.
	barchart() Plot an array s, or a set of points with explicite coordinnates arrays, x, y and z, as a bar chart, eg for histograms. This function is very versatile and will accept 2D or 3D arrays, but also clouds of points, to position the bars.
	triangular_mesh() Plot a triangular mesh, fully specified by x, y and z coordinnates of its vertices, and the (n, 3) array of the indices of the triangles.

Vertical scale of surf() and contour_surf()

surf() and contour_surf() can be used as 3D representation of 2D data. By default the z-axis is supposed to be in the same units as the x and y axis, but it can be auto-scaled to give a 2/3 aspect ratio. This behavior can be controlled by specifying the “warp_scale=’auto’”.

From data points to surfaces.

Knowing the positions of data points is not enough to define a surface, connectivity information is also required. With the functions surf() and mesh(), this connectivity information is implicitely extracted from the shape of the input arrays: neighbooring data points in the 2D input arrays are connected, and the data lies on a grid. With the function triangular_mesh(), connectivity is explicitely specified. Quite often, the connectivity is not regular, but is not known in advance either. The data points lie on a surface, and we want to plot the surface implicitely defined. The delaunay2d filter does the required nearest-neighboor matching, and interpolation, as shown in the surface_from_irregular_data example (Surface from irregular data example).

3D data

	contour3d() Plot isosurfaces of volumetric data defined as a 3D array.
	quiver3d() Plot arrows to represent vectors at data points. The x, y, z position are specified by numpy arrays, as well as the u, v, w components of the vectors.
	flow() Plot trajectories of particles along a vector field described by three 3D arrays giving the u, v, w components on a grid.

Structured or unstructured data

contour3d() and flow() require ordered data (to be able to interpolate between the points), whereas quiver3d() works with any set of points. The required structure is detailed in the functions’ documentation.

Note

Many richer visualisations can be created by assembling data sources filters and modules. See the Assembling pipelines with mlab and the Case studies of some visualizations sections.

Changing the looks of the visual objects created

Adding color or size variations

Color:

The color of the objects created by a plotting function can be specified explicitly using the ‘color’ keyword argument of the function. This color is than applied uniformly to all the objects created.

If you want to vary the color across your visualization, you need to specify scalar information for each data point. Some functions try to guess this information: these scalars default to the norm of the vectors, for functions with vectors, or to the z elevation for functions where is meaningful, such as surf() or barchart().

This scalar information is converted into colors using the colormap, or also called LUT, for Look Up Table. The list of possible colormaps is:

accent       flag          hot      pubu     set2
autumn       gist_earth    hsv      pubugn   set3
black-white  gist_gray     jet      puor     spectral
blue-red     gist_heat     oranges  purd     spring
blues        gist_ncar     orrd     purples  summer
bone         gist_rainbow  paired   rdbu     winter
brbg         gist_stern    pastel1  rdgy     ylgnbu
bugn         gist_yarg     pastel2  rdpu     ylgn
bupu         gnbu          pink     rdylbu   ylorbr
cool         gray          piyg     rdylgn   ylorrd
copper       greens        prgn     reds
dark2        greys         prism    set1

The easiest way to choose the colormap most adapted to your visualization is to use the GUI (as described in the next paragraph). The dialog to set the colormap can be found in the Colors and legends node.

Size of the glyph:  

The scalar information can also be displayed in many different ways. For instance it can be used to adjust the size of glyphs positioned at the data points.

A caveat: Clamping: relative or absolute scaling Given six points positionned on a line with interpoint spacing 1:

x = [1, 2, 3, 4, 5, 6]
y = [0, 0, 0, 0, 0, 0]
z = y

If we represent a scalar varying from 0.5 to 1 on this dataset:

s = [.5, .6, .7, .8, .9, 1]

We represent the dataset as spheres, using points3d(), and the scalar is mapped to diameter of the spheres:

from enthought.mayavi import mlab
pts = mlab.points3d(x, y, z, s)

By default the diameter of the spheres is not ‘clamped’, in other words, the smallest value of the scalar data is represented as a null diameter, and the largest is proportional to inter-point distance. The scaling is only relative, as can be seen on the resulting figure:

This behavior gives visible points for all datasets, but may not be desired if the scalar represents the size of the glyphs in the same unit as the positions specified.

In this case, you shoud turn auto-scaling off by specifying the desired scale factor:

pts = mlab.points3d(x, y, z, s, scale_factor=1)

Warning

In earlier versions of Mayavi (up to 3.1.0 included), the glyphs are not auto-scaled, and as a result the visualization can seem empty due to the glyphs being very small. In addition the minimum diameter of the glyphs is clamped to zero, and thus the glyph are not scaled absolutely, unless you specifie:

pts.glyph.glyph.clamping = False

More representations of the attached scalars or vectors:  

There are many more ways to represent the scalar or vector information attached to the data. For instance, scalar data can be ‘warped’ into a displacement, e.g. using a WarpScalar filter, or the norm of scalar data can be extract to a scalar component that can be visualized using iso-surfaces with the ExtractVectorNorm filter.

Changing the scale and position of objects

Each mlab function takes an extent keyword argument, that allows to set its (x, y, z) extents. This give both control on the scaling in the different directions and the displacement of the center. Beware that when you are using this functionality, it can be useful to pass the same extents to other modules visualizing the same data. If you don’t, they will not share the same displacement and scale.

The surf(), contour_surf(), and bar_chart functions, which display 2D arrays by converting the values in height, also take a warp_scale parameter, to control the vertical scaling.

Changing object properties interactively

Mayavi, and thus mlab, allows you to interactively modify your visualization.

The Mayavi pipeline tree can be displayed by clicking on the mayavi icon in the figure’s toolbar, or by using show_pipeline() mlab command. One can now change the visualization using this dialog by double-clicking on each object to edit its properties, as described in other parts of this manual, or add new modules or filters by using this icons on the pipeline, or through the right-click menus on the objects in the pipeline.

In addition, for every object returned by a mlab function, this_object.edit_traits() brings up a dialog that can be used to interactively edit the object’s properties. If the dialog doesn’t show up when you enter this command, please see Running mlab scripts.

Using mlab with the full Envisage UI

Sometimes it is convenient to write an mlab script but still use the full envisage application so you can click on the menus and use other modules etc. To do this you may do the following before you create an mlab figure:

from enthought.mayavi import mlab
mlab.options.backend = 'envisage'
f = mlab.figure()
# ...

This will give you the full-fledged UI instead of the default simple window.

Figures, legends, camera and decorations

Handling several figures

All mlab functions operate on the current scene, that we also call figure(), for compatibility with matlab and pylab. The different figures are indexed by key that can be an integer or a string. A call to the figure() function giving a key will either return the corresponding figure, if it exists, or create a new one. The current figure can be retrieved with the gcf() function. It can be refreshed using the draw() function, saved to a picture file using savefig() and cleared using clf().

Figure decorations

Axes can be added around a visualization object with the axes() function, and the labels can be set using the xlabel(), ylabel() and zlabel() functions. Similarly, outline() creates an outline around an object. title() adds a title to the figure.

Color bars can be used to reflect the color maps used to display values (LUT, or lookup tables, in VTK parlance). colorbar() creates a color bar for the last object created, trying to guess whether to use the vector data or the scalar data color maps. The scalarbar() and vectorbar() function scan be used to create color bars specifically for scalar or vector data.

A small xyz triad can be added to the figure using orientation_axes().

Warning

The orientation_axes() was named orientationaxes before release 3.2.

Moving the camera

The position and direction of the camera can be set using the view() function. They are described in terms of Euler angles and distance to a focal point. The view() function tries to guess the right roll angle of the camera for a pleasing view, but it sometimes fails. The roll() explicitly sets the roll angle of the camera (this can be achieve intercactively in the scene by pressing down the control key, while dragging the mouse, see Interaction with the scene).

The view() and roll() functions return the current values of the different angles and distances they take as arguments. As a result, the view point obtained interactively can be stored an reset using:

# Store the information
view = mlab.view()
roll = mlab.roll()

# Reposition the camera
mlab.view(*view)
mlab.roll(roll)

Rotating the camera around itself

You can also rotate the camera around itself using the roll, yaw and pitch methods of the camera object. This moves the focal point:

f = mlab.gcf()
camera = f.scene.camera
camera.yaw(45)

Unlike the mlab.view() and mlab.roll() function, the angles are incremental, and not absolute.

Modifying zoom and view angle

The camera is entirely defined by its position, its focal point, and its view angle (attributes ‘position’, ‘focal_point’, ‘view_angle’). The camera method ‘zoom’ changes the view angle incrementally by the specify ratio, where as the method ‘dolly’ translates the camera along its axis while keeping the focal point constant.

Running mlab scripts

Mlab, like the rest of Mayavi, is an interactive application. If you are not already in an interactive environment (see next paragraph), to interact with the figures or the rest of the drawing elements, you need to use the show() function. For instance, if you are writing a script, you need to call show() each time you want to display one or more figures and allow the user to interact with them.

Using mlab interactively

Using `IPython`_ mlab instructions can be run interactively, or in scripts using `IPython`_‘s %run command:

In [1]: %run my_script

You need to start `IPython`_ with the -wthread option (when installed with EPD, the pylab start-menu link does this for you). In this environment, the plotting commands are interactive: they have an immediate effect on the figure, alleviating the need to use the show() function.

Mlab can also be used interactively in the Python shell of the mayavi2 application, or in any interactive Python shell of wxPython-based application (such as other Envisage-based applications, or SPE, Stani’s Python Editor).

Using together with Matplotlib’s pylab

If you want to use Matplotlib’s pylab with Mayavi’s mlab in IPython you should:

• if your IPython version is greater than 0.8.4: start IPython with the following options:

  $ ipython -pylab -wthread

• elsewhere, start IPython with the -wthread option:

  $ ipython -wthread

  and before importing pylab, enter the following Python commands:

  >>> import matplotlib
  >>> matplotlib.use('WxAgg')
  >>> matplotlib.interactive(True)
  

If you want matplotlib and mlab to work together by default in IPython, you can change you default matplotlib backend, by editing the ~/.matplotlib/matplotlibrc to add the following line:

backend     : WXAgg

In scripts

Mlab commands can be written to a file, to form a script. This script can be loaded in the Mayavi application using the File->Open file menu entry, and executed using the File->Refresh code menu entry or by pressing Control-r. It can also be executed during the start of the Mayavi application using the -x command line switch.

As mentioned above, when running outside of an interactive environment, for instance with python myscript.py, you need to call the show() function (as shown in the demo above) to pause your script and have the user interact with the figure.

You can also use show() to decorate a function, and have it run in the event-loop, which gives you more flexibility:

from enthought.mayavi import mlab
from numpy import random

@mlab.show
def image():
   mlab.imshow(random.random((10, 10)))

With this decorator, each time the image function is called, mlab makes sure an interactive environment is running before executing the image function. If an interactive environment is not running, mlab will start one and the image function will not return until it is closed.

Animating the data

Often it isn’t sufficient to just plot the data. You may also want to change the data of the plot and update the plot without having to recreate the entire visualization, for instance to do animations, or in an interactive application. Indeed, recreating the entire visualization is very inefficient and leads to very jerky looking animations. To do this, mlab provides a very convenient way to change the data of an existing mlab visualization. Consider a very simple example. The mlab.test_simple_surf_anim function has this code:

x, y = numpy.mgrid[0:3:1,0:3:1]
s = mlab.surf(x, y, numpy.asarray(x*0.1, 'd'))

for i in range(10):
    s.mlab_source.scalars = numpy.asarray(x*0.1*(i+1), 'd')

The first two lines define a simple plane and view that. The next three lines animate that data by changing the scalars producing a plane that rotates about the origin. The key here is that the s object above has a special attribute called mlab_source. This sub-object allows us to manipulate the points and scalars. If we wanted to change the x values we could set that too by:

s.mlab_source.x = new_x

The only thing to keep in mind here is that the shape of x should not be changed.

If multiple values have to be changed, you can use the set method of the mlab_source to set them as shown in the more complicated example below:

# Produce some nice data.
n_mer, n_long = 6, 11
pi = numpy.pi
dphi = pi/1000.0
phi = numpy.arange(0.0, 2*pi + 0.5*dphi, dphi, 'd')
mu = phi*n_mer
x = numpy.cos(mu)*(1+numpy.cos(n_long*mu/n_mer)*0.5)
y = numpy.sin(mu)*(1+numpy.cos(n_long*mu/n_mer)*0.5)
z = numpy.sin(n_long*mu/n_mer)*0.5

# View it.
l = plot3d(x, y, z, numpy.sin(mu), tube_radius=0.025, colormap='Spectral')

# Now animate the data.
ms = l.mlab_source
for i in range(10):
    x = numpy.cos(mu)*(1+numpy.cos(n_long*mu/n_mer +
                                      numpy.pi*(i+1)/5.)*0.5)
    scalars = numpy.sin(mu + numpy.pi*(i+1)/5)
    ms.set(x=x, scalars=scalars)

Notice the use of the set method above. With this method, the visualization is recomputed only once. In this case, the shape of the new arrays has not changed, only their values have. If the shape of the array changes then one should use the reset method as shown below:

x, y = numpy.mgrid[0:3:1,0:3:1]
s = mlab.surf(x, y, numpy.asarray(x*0.1, 'd'),
              representation='wireframe')
# Animate the data.
fig = mlab.gcf()
ms = s.mlab_source
for i in range(5):
    x, y = numpy.mgrid[0:3:1.0/(i+2),0:3:1.0/(i+2)]
    sc = numpy.asarray(x*x*0.05*(i+1), 'd')
    ms.reset(x=x, y=y, scalars=sc)
    fig.scene.reset_zoom()

Many standard examples for animating data are provided with mlab. Try the examples with the name mlab.test_<name>_anim, i.e. where the name ends with an _anim to see how these work and run.

Note

It is important to remember distinction between set and reset. Use set or directly set the attributes (x, y, scalars etc.) when you are not changing the shape of the data but only the values. Use reset when the arrays are changing shape and size. Reset usually regenerates all the data and can be inefficient when compared to set or directly setting the traits.

When creating a Mayavi pipeline, as explained in the following subsection, instead of using ready-made plotting function, the mlab_source attribute is created only on sources created via mlab. Only pipeline created entirely using mlab will present this attribute.

Assembling pipelines with mlab

The plotting functions reviewed above explore only a small fraction of the visualization possibilities of Mayavi. The full power of Mayavi can only be unleashed through the control of the pipeline itself. As described in the An overview of Mayavi section, a visualization in Mayavi is created by loading the data in Mayavi with data source object, optionally transforming the data through Filters, and visualizing it with Modules. The mlab functions build complex pipelines for you in one function, making the right choice of sources, filters, and modules, but they cannot explore all the possible combinations.

Mlab provides a submodule pipeline which contains functions to populate the pipeline easily from scripts. This module is accessible in mlab: mlab.pipeline, or can be imported from enthought.mayavi.tools.pipeline.

When using an mlab plotting function, a pipeline is created: first a source is created from numpy arrays, then modules, and possibly filters, are added. The resulting pipeline can be seen for instance with the mlab.show_pipeline command. This information can be used to create the very same pipeline using directly the pipeline scripting module, as the names of the functions required to create each step of the pipeline are directly linked to the default names of the objects created by mlab on the pipeline. As an example, let us create a visualization using surf():

import numpy as np
a = np.random.random((4, 4))
from enthought.mayavi import mlab
mlab.surf(a)
mlab.show_pipeline()

The following pipeline is created:

Array2DSource
    \__ WarpScalar
            \__ PolyDataNormals
                    \__ Colors and legends
                            \__ Surface

The same pipeline can be created using the following code:

src = mlab.pipeline.array2d_source(a)
warp = mlab.pipeline.warp_scalar(src)
normals = mlab.pipeline.poly_data_normals(warp)
surf = mlab.pipeline.surface(normals)

Data sources

The pipeline module contains functions for creating various data sources from arrays. They are fully documented in details in the Mlab pipeline-control reference. We give a small summary of the possibilities here.

mlab distinguishes sources with scalar data, and sources with vector data, but more important, it has different functions to create sets of unconnected points, with data attached to them, or connected data points describing continuously varying quantities that can be interpolated between data points, often called fields in physics or engineering.

Unconnected sources:  scalar_scatter(), vector_scatter() Implicitely-connected sources:  scalar_field(), vector_field(), array2d_source() Explicitly-connected sources:  line_source(), triangular_mesh_source()

All the mab source factories are functions that take numpy arrays and return the Mayavi source object that was added to the pipeline. However, the implicitely-connected sources require well-shaped arrays as arguments: the data is supposed to lie on a regular, orthogonal, grid of the same shape as the shape of the input array, in other words, the array describes an image, possibly 3 dimensional.

Modules and filters

For each Mayavi module or filter (see Modules and Filters), there is a corresponding mlab.pipeline function. The name of this function is created by replacing the alternating capitals in the module or filter name by underscores. Thus ScalarCutPlane corresponds to scalar_cut_plane.

In general, the mlab.pipeline module and filter factory functions simply create and connect the corresponding object. However they can also contain addition logic, exposed as keyword arguments. For instance they allow to set up easily a colormap, or to specify the color of the module, when relevant. In accordance with the goal of the mlab interface to make frequent operations simple, they use the keyword arguments to choose the properties of the create object to best suit the requirements. It can be thus easier to use the keyword arguments, when available, than to set the attributes of the objects created. For more information, please check out the docstrings. Full, detailed, usage examples are given in the next subsection.

Case studies of some visualizations

Visualizing volumetric scalar data

There are three main ways of visualizing a 3D scalar field. Given the following field:

import numpy as np
x, y, z = np.ogrid[-10:10:20j, -10:10:20j, -10:10:20j]
s = np.sin(x*y*z)/(x*y*z)

IsoSurfaces:

To display iso surfaces of the field, the simplest solution is simply to use the mlab contour3d() function:

mlab.contour3d(s)

The problem with this method that outer iso-surfaces tend to hide inner ones. As a result, quite often only one iso-surface can be visible.

Volume rendering:  

Volume rendering is an advanced technique in which each voxel is given a partly transparent color. This can be achieved with mlab.pipeline using the scalar_field() source, and the volume module:

mlab.pipeline.volume(mlab.pipeline.scalar_field(s))

It is useful to open the module’s dialog (eg through the pipeline interface, or using it’s edit_traits() method) and tweak the color transfert function to render transparent the low-intensities regions of the image. For this module, the LUT as defined in the `Colors and legends` node are not used

The limitations of volume rendering is that, while it is often very pretty, it can be difficult to analysis the details of the field with it.

Cut planes:

While less impressive, cut planes are a very informative way of visualising the details of a scalar field:

mlab.pipeline.image_plane_widget(mlab.pipeline.scalar_field(s),
                            plane_orientation='x_axes',
                            slice_index=10,
                        )
mlab.pipeline.image_plane_widget(mlab.pipeline.scalar_field(s),
                            plane_orientation='y_axes',
                            slice_index=10,
                        )
mlab.outline()

The image plane widget can only be used on regular-spaced data, as created by mlab.pipeline.scalar_field, but it is very fast. It should thus be prefered to the scalar cut plane, when possible.

Clicking and dragging the cut plane is an excellent way of exploring the field.

A combination of techniques:  

Finally, it can be interesting to combine cut planes with iso-surfaces and thresholding to give a view of the peak areas using the iso-surfaces, visualize the details of the field with the cut plane, and the global mass with a large iso-surface:

src = mlab.pipeline.scalar_field(s)
mlab.pipeline.iso_surface(src, contours=[s.min()+0.1*s.ptp(), ], opacity=0.1)
mlab.pipeline.iso_surface(src, contours=[s.max()-0.1*s.ptp(), ],)
mlab.pipeline.image_plane_widget(src,
                            plane_orientation='z_axes',
                            slice_index=10,
                        )

In some cases, thought not in our example, it might be usable to insert a threshold filter before the cut plane, eg to remove area with values below ‘s.min()+0.1*s.ptp()’. In this case, the cut plane needs to be implemented with mlab.pipeline.scalar_cut_plane as the data looses its structure after thresholding.

Visualizing a vector field

A vector field, ie vectors continuously defined in a volume, can be difficult to visualize, as it contains a lot of information. Let us explore different visualizations for the velocity field of a multi-axis convection cell [1], in hydrodynamics, as defined by its components sampled on a grid, u, v, w:

import numpy as np
x, y, z = np.mgrid[0:1:20j, 0:1:20j, 0:1:20j]

u =    np.sin(np.pi*x) * np.cos(np.pi*z)
v = -2*np.sin(np.pi*y) * np.cos(2*np.pi*z)
w = np.cos(np.pi*x)*np.sin(np.pi*z) + np.cos(np.pi*y)*np.sin(2*np.pi*z)

Quiver:

The simplest visualization of a set of vectors, is using the mlab function quiver3d:

mlab.quiver3d(u, v, w)
mlab.outline()

The main limitation of this visualization is that it positions an arrow for each sampling point on the grid. As a result the visualization is very busy.

Masking vectors:  

We can use the fact that we are visualizing a vector field, and not just a bunch of vectors, to reduce the amount of arrows displayed. For this we need to build a vector_field source, and apply to it the vectors module, with some masking parameters (here we keep only one point out of 20):

src = mlab.pipeline.vector_field(u, v, w)
mlab.pipeline.vectors(src, mask_points=20, scale_factor=3.)

A cut plane:

If we are interested in displaying the vectors along a cut, we can use a cut plane. In particular, we can inspect interactively the vector field by moving the cut plane along: clicking on it and dragging it can give a very clear understanding of the vector field:

mlab.pipeline.vector_cut_plane(src, mask_points=2, scale_factor=3)

IsoSurfaces of the magnitude:  

An important parameter of the vector field is its magnitude. It can be interesting to display iso-surfaces of the norm of the vectors. For this we can create a scalar field from the vector field using the ExtractVectorNorm filter, and use the IsoSurface module on it. When working interactively, a good understanding of the magnitude of the field can be gained by changing the values of the contours in the object’s property dialog.

magnitude = mlab.pipeline.extract_vector_norm(src)
mlab.pipeline.iso_surface(magnitude, contours=[1.9, 0.5])

The Flow, or the field lines:  

For certain vector fields, the line of flow of along the field can have an interesting meaning. For instance the can be interpreted as trajectories in hydrodynamics, or field lines in electro-magnetism. We can display the flow lines originating for a certain seed surface using the streamline module, or the mlab flow function, which calls it:

flow = mlab.flow(u, v, w, seed_scale=1,
                          seed_resolution=5,
                          integration_direction='both')

A combination of techniques:  

Giving a meaningful visualization of a vector field is a hard task, and one must use all the tools at hand to illustrate his purposes. It is important to choose the message conveyed. No one visualization will tell all about a vector field. Here is an example of a visualization made by combining the different tools above:

mlab.figure(fgcolor=(0., 0., 0.), bgcolor=(1, 1, 1))
src = mlab.pipeline.vector_field(u, v, w)
magnitude = mlab.pipeline.extract_vector_norm(src)

# We apply the following modules on the magnitude object, in order to
# be able to display the norm of the vectors, eg as the color.
iso = mlab.pipeline.iso_surface(magnitude, contours=[1.9, ], opacity=0.3)

vec = mlab.pipeline.vectors(magnitude, mask_points=40,
                                    line_width=1,
                                    color=(.8, .8, .8),
                                    scale_factor=4.)

flow = mlab.pipeline.streamline(magnitude, seedtype='plane',
                                        seed_visible=False,
                                        seed_scale=0.5,
                                        seed_resolution=1,
                                        linetype='ribbon',)

vcp = mlab.pipeline.vector_cut_plane(magnitude, mask_points=2,
                                        scale_factor=4,
                                        colormap='jet',
                                        plane_orientation='x_axes')

Note

Although most of this section has been centered on snippets of code to create visualization objects, it is important to remember that Mayavi is an interactive program, and that the properties of these objects can be modified interactively, as described in Changing object properties interactively. It is often impossible to choose the best parameters for a visualization before hand. Colors, contour values, colormap, view angle, etc... should be chosen interactively. If reproducibility is required, the chosen values can be added in the original script.

Moreover, the mlab functions expose only a small fraction of the possibilities of the visualization objects. The dialogs expose more of these functionalities, that are entirely controlled by the attributes of the objects returned by the mlab functions. These objects are very rich, as they are built from VTK objects. It can be hard to find the right attribute to modify when exploring them, or in the VTK documentation, thus using the interactive dialog and recording to a script, as described in Recording Mayavi actions to a script is the prefered way of tweaking a visualization.

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[1]	Toussaint, V.; Carriere, P. & Raynal, F. A numerical Eulerian approach to mixing by chaotic advection Phys. Fluids, 1995, 7, 2587