Material for tutorial. Twitter: prabhu_r. Slides: Demos:

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1 Material for tutorial Twitter: prabhu_r Slides: Demos:

2 3D Data visualization with Mayavi Prabhu Ramachandran Gaël Varoquaux Department of Aerospace Engineering IIT Bombay SciPy.in 2011, December 7, IIT Bombay. Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 2 / 72

3 Objectives At the end of this session you will be able to: 1 Use mlab effectively to visualize numpy array data of various kinds 2 Apply some of mayavi s advanced features 3 Embed mayavi visualizations in your dialogs 4 Create TVTK datasets for more effective visualization (if time permits)

4 Outline 1 Quick introduction to Mayavi 2 mlab 3 Embedding mayavi 4 Creating and working with datasets Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 4 / 72

6 Who are we? Prabhu Ramachandran 2001 Creator and lead Gaël Varoquaux 2007 mlab, documentation, usability Enthought Inc. ETS, Hosting, support, sprints, initial funding, distribution Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 6 / 72

7 History Mayavi-1.x: 2001 TVTK: 2004, Enthought Mayavi2: 2005, Enthought, IITB 2008: Mayavi sprint at Austin Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 7 / 72

8 Overview of features

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10 Live in your dialogs

11 Mayavi in applications

12 Exploring the documentation

13 Other features Easy customization Offscreen animations Automatic script generation Powerful command line options

14 Summary mayavi Uses VTK ( BSD license Linux, win32 and Mac OS X Highly scriptable Embed in Traits UIs (wxpython and PyQt4) Envisage Plugins Debian/Ubuntu/Fedora Pythonic 15

16 Overview Simple Convenient Full-featured Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 16 / 72

17 Getting started Vanilla: $ ipython wthread with Pylab: $ ipython pylab wthread

18 Using mlab: >>> from enthought. mayavi import mlab Try these: >>> mlab. test_ <TAB> >>> mlab. test_contour3d ( ) >>> mlab. test_contour3d??

19 Exploring the view Mouse Keyboard Toolbar Mayavi icon 20

20 mlab plotting functions 0D data >>> from numpy import >>> t = l i nspace ( 0, 2 pi, 50) >>> u = cos ( t ) p i >>> x, y, z = s i n ( u ), cos ( u ), s i n ( t ) >>> mlab.points3d(x, y, z)

21 Changing how things look Clearing the view >>> mlab.clf() IPython is your friend! >>> mlab.points3d? Extra argument: Scalars Keyword arguments UI >>> mlab. points3d ( x, y, z, t, scale_mode= none )

24 1D data >>> mlab.plot3d(x, y, z, t ) Plots lines between the points

25 2D data >>> x = mgrid [ 3:3:100 j, 3:3:100 j ] >>> z = s i n ( x x + y y ) >>> mlab.surf(x, y, z) Assumes the points are rectilinear

26 2D data: mlab.mesh >>> mlab.mesh(x, y, z) Points needn t be regular >>> phi, t h e t a = numpy. mgrid [ 0 : p i :20 j,... 0:2 p i :20 j ] >>> x = s i n ( phi ) cos ( t h e t a ) >>> y = s i n ( phi ) s i n ( t h e t a ) >>> z = cos ( phi ) >>> mlab. mesh( x, y, z,... r e p r e s e n t a t i o n = wireframe )

27 3D data >>> x, y, z = o g r i d [ 5:5:64 j,... 5:5:64 j,... 5:5:64 j ] >>> mlab. contour3d ( x x y y + z z 2)

28 3D vector data: mlab.quiver3d >>> mlab. t e s t _ q u i v e r 3 d ( ) obj = mlab.quiver3d(x, y, z, u, v, w) 50

29 Exercise: Lorenz equation dx dt dy dt dz dt = s(y x) = rx y xz = xy bz Let s = 10, r = 28, b = 8./3. Region of interest x, y, z = mgrid [ 50:50:20 j, 50:50:20 j, 10:60:20 j ] Use mlab.quiver3d

30 mlab. quiver3d ( x, y, z, u, v, w, s c a l e _ f a c t o r =0.01, mask_points =5) mlab. show ( ) Solution def lorenz ( x, y, z, s =10., r =28., b = 8. / 3. ) : u = s ( y x ) v = r x y x z w = x y b z return u, v, w x, y, z = mgrid [ 50:50:20 j, 50:50:20 j, 10:60:20 j ] u, v, w = lorenz ( x, y, z )

31 Issues and solutions Basic visualization: not very useful Tweak parameters: mask_points, scale_factor Explore parameters on UI mlab.flow is a lot better! Good visualization involves work 60

32 Other utility functions gcf: get current figure savefig, figure axes, outline title, xlabel, ylabel, zlabel colorbar, scalarbar, vectorbar show: Standalone mlab scripts Others, see UG

39 Can we do more? Yes!

40 quiver3d ( x, y, z, u, v, w, s c a l e _ f a c t o r =0.01, mask_points =5)

41 Looking inside

42 The pipeline 70

43 Mayavi Engine TVTK Scene Source Filter ModuleManager Lookup tables List of Modules

44 Changing the pipeline On UI Right click on node drag drop Script Or use mlab.pipeline Example: mlab.pipeline. outline () obj.remove()

45 Exercise >>> mlab. t e s t _ q u i v e r 3 d ( ) Hide vectors, add a Vector Cut Plane >>> mlab. t e s t _ f l o w ( ) Add a Vector Cut Plane Can also use the Lorenz example

46 Exercise >>> mlab. t e s t _ q u i v e r 3 d ( ) Hide vectors, add a Vector Cut Plane >>> mlab. t e s t _ f l o w ( ) Add a Vector Cut Plane Can also use the Lorenz example

47 Surprised?

48 So what is the problem?

49 Points?

50 Curve?

51 Surface?

52 Interior of sphere?

53 Datasets Quiver v/s Flow Get back to this later! 85

54 Recap mlab gets you started Pipeline and data flow Datasets are important

55 Changing the pipeline On UI Right click on node drag drop Script Or use mlab.pipeline Example: mlab.pipeline. outline () obj.remove()

56 mlab and Mayavi2? mlab is just a thin layer over the Mayavi OO API mlab commands return mayavi objects

57 Exercise 1 Start with flow for the Lorenz system 2 Now extract the vector norm (use a filter) 3 Plot iso-contours of this 4 Figure out how to do this from the UI and mlab.pipeline 95 Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 48 / 72

58 So how do you make a fancier script? Use script recording Demo

59 So how do you make a fancier script? Use script recording Demo

60 Animating data >>> s = mlab. flow ( x, y, z, u, v, w) >>> s. mlab_source. u = u z mlab_source.set: multiple attributes If you change the shape of the arrays use the reset method

61 Setting the view >>> p r i n t mlab. view ( ) >>> mlab. view ( azimuth=none, e l e v a t i o n =None, distance=none, f o c a l p o i n t =None ) 110

63 General approach Embed Mayavi into a dialog box Use traits to wire up everything Full power of mayavi at your disposal

64 Simple example 120

65 Exercise: Lorenz trajectory Use the provided skeleton script 1 Create a simple UI to show a trajectory 2 Create sliders to change the position of the initial condition 3 Create a UI element to change the integration time 125 Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 55 / 72

67 Motivation Datasets are fundamental to doing visualization correctly Motivational problem Atmospheric data of temperature over the surface of the earth. Let temperature (T ) vary linearly with height (z): T = z

68 Simple solution l a t = l inspace ( 89, 89, 37) lon = l i n space ( 0, 360, 37) z = l i n s p ace ( 0, 100, 11) x, y, z = mgrid [0:360:37 j, 89:89:37 j, 0:100:11 j ] t = z mlab. contour3d ( x, y, z, t ) mlab. o u t l i n e ( ) mlab. c o l o r b a r ( )

69 Simple solution l a t = l inspace ( 89, 89, 37) lon = l i n space ( 0, 360, 37) z = l i n s p ace ( 0, 100, 11) x, y, z = mgrid [0:360:37 j, 89:89:37 j, 0:100:11 j ] t = z mlab. contour3d ( x, y, z, t ) mlab. o u t l i n e ( ) mlab. c o l o r b a r ( )

70 What happens underneath? P = mlab. p i p e l i n e src = P. s c a l a r _ f i e l d ( x, y, z, t ) i s o = P. iso_surface ( src ) # Try t h i s. p r i n t src

71 The underlying dataset from enthought. t v t k. api import t v t k o r i g = ( 0, 90, 0) spacing = (10, 5, 10) dims = (37, 37, 11) i d = t v t k. ImageData ( o r i g i n = orig, spacing =spacing, dimensions=dims ) i d. point_data. s c a l a r s = t. T. f l a t t e n ( ) i d. point_data. s c a l a r s. name = T # View i t. src = P. add_dataset ( i d ) i s o = P. iso_surface ( src )

72 The general idea Specify the points (explicitly or implicitly) Specify the connectivity between the points (explicit/implicit) The connectivity lets you build cells that break the space into pieces Specify attribute data at the points or cells Points Rectangular cell Triangular cells Point data Cell data 20 10

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74 Types of datasets Implicit topology (structured): Image data (structured points) Rectilinear grids Structured grids Explicit topology (unstructured): Polygonal data (surfaces) Unstructured grids

75 Implicit versus explicit topology Implicit topology associated with points: The X co-ordinate increases first, Y next and Z last Easiest example: a rectangular mesh Non-rectangular mesh certainly possible Prabhu Ramachandran, Gaël Varoquaux (IIT Bombay) Mayavi2 tutorial 64 / 72

76 On a sphere? lon, l a t, ht = x p i /180, (90+y ) p i /180, z r = ( ht ) tmp = r s i n ( l a t ) # Points on the sphere x, y, z = tmp cos ( lon ), tmp s i n ( lon ), r cos ( l a t ) pts = empty ( x. shape + ( 3, ), dtype= f l o a t ) pts [..., 0 ] = x pts [..., 1 ] = y pts [..., 2 ] = z # Reorder the p o i n t s / s c a l a r s f o r VTK pts = pts. transpose ( 2, 1, 0, 3 ). copy ( ) pts. shape = pts. size / 3, 3 t = t. T. copy ( )

77 sg = t v t k. S t r u c t u r e d G r i d ( ) sg. dimensions = x. shape sg. p o i n t s = pts sg. point_data. s c a l a r s = t. r a v e l ( ) sg. point_data. s c a l a r s. name = T P = mlab. p i p e l i n e src = P. add_dataset ( sg ) P. grid_plane ( src ) P. iso_surface ( src, contours =1) mlab. show ( )

78 # Save a dataset to disk. from enthought. t v t k. api import w r i t e _ d a t a w r i t e _ d a t a ( dataset, fname ) # Open back t h e data. mlab. p i p e l i n e. open ( fname ) Try right clicking a node!

79 Unstructured grids Explicit topology specification Specified via connectivity lists Different number of neighbors, different types of cells

80 PolyData from enthought. t v t k. api import t v t k # The p o i n t s i n 3D. p o i n t s = array ( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], f ) # C o n n e c t i v i t y v i a i n d i c e s to the p o i n t s. t r i a n g l e s = array ( [ [ 0, 1, 3 ], [ 0, 3, 2 ], [ 1, 2, 3 ], [ 0, 2, 1 ] ] ) # Creating the data o b j e c t. mesh = t v t k. PolyData ( ) mesh. p o i n t s = p o i n t s # the p o i n t s mesh. polys = t r i a n g l e s # t r i a n g l e s f o r c o n n e c t i v i t y # For l i n e s use : mesh. l i n e s = l i n e s # Now create some p o i n t data. temperature = array ( [ 1 0, 20,20, 30], f ) mesh. point_data. s c a l a r s = temperature mesh. point_data. s c a l a r s. name = temperature

81 PolyData from enthought. t v t k. api import t v t k # The p o i n t s i n 3D. p o i n t s = array ( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], f ) # C o n n e c t i v i t y v i a i n d i c e s to the p o i n t s. t r i a n g l e s = array ( [ [ 0, 1, 3 ], [ 0, 3, 2 ], [ 1, 2, 3 ], [ 0, 2, 1 ] ] ) # Creating the data o b j e c t. mesh = t v t k. PolyData ( ) mesh. p o i n t s = p o i n t s # the p o i n t s mesh. polys = t r i a n g l e s # t r i a n g l e s f o r c o n n e c t i v i t y # For l i n e s use : mesh. l i n e s = l i n e s # Now create some p o i n t data. temperature = array ( [ 1 0, 20,20, 30], f ) mesh. point_data. s c a l a r s = temperature mesh. point_data. s c a l a r s. name = temperature

82 Summary 140

83 Advanced features Command line arguments, timeseries, scripting

84 Thank you!