3d data visualization with mayavi and...

3D Data visualization with Mayaviand TVTK

Prabhu Ramachandran

Department of Aerospace EngineeringIIT Bombay

Advanced tutorials at SciPy09Caltech, Pasadena

Aug. 18, 2009

Prabhu Ramachandran (IIT Bombay) Mayavi2 tutorial 1 / 73

Objectives

At the end of this session you will be able to:1 Use mlab effectively to visualize numpy array data

of various kinds2 Apply some of mayavi’s advanced features3 Embed mayavi visualizations in your dialogs4 Create TVTK datasets for more effective

visualization (if time permits)

Outline

1 Quick introduction to Mayavi

2 mlab

3 Embedding mayavi

4 Creating and working with datasets

Outline

2 mlab

3 Embedding mayavi

Who are we?

Prabhu Ramachandran Creator and lead, 2001 –Gaël Varoquaux Mlab, documentation, usability,

2007 –Enthought Inc. ETS, Hosting, support, sprints,

initial funding, distribution

History

Mayavi-1.x: 2001TVTK: 2004, EnthoughtMayavi2: 2005, Enthought, IITB2008: Mayavi sprint

Overview of features

mlab: interactive work

from enthought . mayavi import mlabfrom numpy import ogr idx , y , z = ogr id [ −5:5:64 j ,

−5:5:64 j ,−5:5:64 j ]

mlab . contour3d ( x∗x∗0.5 + y∗y +z∗z∗2)

mlab . show ( )

Live in your dialogs

Mayavi in applications

Exploring the documentation

Other features

Easy customizationOffscreen animationsAutomatic script generationPowerful command line options

Summary

http://code.enthought.com/projects/mayavi

Uses VTK (www.vtk.org)BSD licenseLinux, win32 and Mac OS XHighly scriptableEmbed in Traits UIs (wxPython and PyQt4)Envisage PluginsDebian/Ubuntu/FedoraPythonic

Outline

2 mlab

3 Embedding mayavi

Overview

SimpleConvenientFull-featured

Getting started

Vanilla:$ ipy thon −wthread

with Pylab:$ ipy thon −pylab −wthread

Using mlab:

>>> from enthought . mayavi import mlab

Try these:

>>> mlab . tes t_ <TAB>>>> mlab . tes t_contour3d ( )>>> mlab . tes t_contour3d ??

Exploring the view

MouseKeyboardToolbarMayavi icon

mlab plotting functions

0D data

>>> from numpy import ∗>>> t = l inspace (0 , 2∗pi , 50)>>> u = cos ( t )∗ p i>>> x , y , z = s in ( u ) , cos ( u ) , s in ( t )

>>> mlab.points3d(x, y, z)

Changing how things look

Clearing the view>>> mlab.clf()

IPython is your friend!>>> mlab.points3d?

Extra argument: ScalarsKeyword argumentsUI

>>> mlab . po in ts3d ( x , y , z , t ,scale_mode= ’ none ’ )

1D data

>>> mlab.plot3d(x, y, z, t )

Plots lines between the points

2D data

>>> x = mgrid [ −3:3:100 j , −3:3:100 j ]>>> z = s in ( x∗x + y∗y )

>>> mlab.surf(x, y, z)

Assumes the points are rectilinear

2D data: mlab.mesh

>>> mlab.mesh(x, y, z)

Points needn’t be regular

>>> phi , the ta = numpy . mgrid [ 0 : p i :20 j ,. . . 0:2∗ p i :20 j ]>>> x = s in ( ph i )∗ cos ( the ta )>>> y = s in ( ph i )∗ s in ( the ta )>>> z = cos ( ph i )>>> mlab . mesh( x , y , z ,. . . r ep resen ta t i on = ’ wireframe ’ )

3D data

>>> x , y , z = ogr id [ −5:5:64 j ,. . . −5:5:64 j ,. . . −5:5:64 j ]>>> mlab . contour3d ( x∗x∗0.5 + y∗y +

z∗z∗2)

3D vector data: mlab.quiver3d

>>> mlab . tes t_qu ive r3d ( )

obj = mlab.quiver3d(x, y, z, u, v, w)

3D vector data: mlab.flow

>>> x , y , z = mgrid [ −2:3 , −2:3 , −2:3]>>> r = s q r t ( x∗∗2 + y∗∗2 + z∗∗4)>>> u = y∗ s in ( r ) / ( r +0.001)>>> v = −x∗ s in ( r ) / ( r +0.001)>>> w = ze ros_ l i ke ( z )>>> ob j = mlab . f low ( x , y , z , u , v , w,

seedtype= ’ plane ’ )>>> ob j . s t ream_tracer . i n t e g r a t o r _ t y p e = \

’ runge_kutta45 ’

Exercise: Lorenz equationdxdt

= s(y − x)

= rx − y − xz

= xy − bz

Let s = 10, r = 28, b = 8./3.

Region of interestx , y , z = mgrid [ −50:50:20 j , −50:50:20 j ,

−10:60:20 j ]

Use mlab.quiver3d

Solutiondef l o renz ( x , y , z , s =10. , r =28. , b = 8 . / 3 . ) :

u = s ∗ ( y−x )v = r ∗x −y − x∗zw = x∗y − b∗zreturn u , v , w

x , y , z = mgrid [ −50:50:20 j , −50:50:20 j ,−10:60:20 j ]

u , v , w = lo renz ( x , y , z )

# Your p l o t here#mlab . show ( )

Issues and solutions

Basic visualization: not very usefulTweak parameters:mask_points, scale_factorExplore parameters on UImlab.flow is a lot better!

Good visualization involves work

Other utility functions

gcf: get current figuresavefig, figureaxes, outlinetitle , xlabel , ylabel , zlabel

colorbar, scalarbar, vectorbarshow: Standalone mlab scriptsOthers, see UG

Can we do more?

quiver3d ( x , y , z ,u , v , w,sca l e_ fac to r =0.01 ,mask_points =5)

Looking inside

The pipeline

Lookup tables

List of Modules

TVTK Scene

Filter

Source

Mayavi Engine

ModuleManager

Changing the pipeline

On UIRight click on nodedrag drop

Script

Or use mlab.pipelineExample: mlab.pipeline. outline ()obj.remove()

Exercise

Hide vectors, add a Vector Cut Plane

>>> mlab . t e s t _ f l o w ( )

Add a Vector Cut Plane

Exercise

Hide vectors, add a Vector Cut Plane

>>> mlab . t e s t _ f l o w ( )

Add a Vector Cut Plane

Surprised?

So what is the problem?

Points?

Curve?

Surface?

Interior of sphere?

Datasets

Quiver v/s Flow

Get back to this later!70

mlab gets you startedPipeline and data flowDatasets are important

Changing the pipeline

On UIRight click on nodedrag drop

Script

Or use mlab.pipelineExample: mlab.pipeline. outline ()obj.remove()

mlab and Mayavi2?

mlab is just a thin layer over the Mayavi OO APImlab commands return mayavi objects

Exercise

1 Start with flow for the Lorenz system2 Now extract the vector norm (use a filter)3 Plot iso-contours of this4 Figure out how to do this from the UI and

mlab.pipeline

So how do you make a fancier script?

Use script recordingDemo

So how do you make a fancier script?

Use script recordingDemo

Animating data

>>> s = mlab . f low ( x , y , z , u , v , w)>>> s . mlab_source . u = u∗z

mlab_source.set: multiple attributesIf you change the shape of the arrays use the resetmethod

Setting the view

>>> pr in t mlab . view ( )>>> mlab . view ( azimuth=None ,

e l ev a t i on =None ,d is tance=None ,f o c a l p o i n t =None )

Outline

2 mlab

3 Embedding mayavi

General approach

Embed Mayavi into a dialog boxUse traits to wire up everythingFull power of mayavi at your disposal

Simple example

Exercise: Lorenz trajectory

Use the provided skeleton script1 Create a simple UI to show a trajectory2 Create sliders to change the position of the initial

condition3 Create a UI element to change the integration time

Outline

2 mlab

3 Embedding mayavi

Motivation

Datasets are fundamental to doing visualizationcorrectly

Motivational problemAtmospheric data of temperature over the surface ofthe earth.Let temperature (T ) vary linearly with height (z):

T = 288.15 − 6.5z

Simple solution

l a t = l inspace (−89, 89 , 37)lon = l inspace (0 , 360 , 37)z = l inspace (0 , 100 , 11)

x , y , z = mgrid [0 :360 :37 j , −89:89:37 j ,0:100:11 j ]

t = 288.15 − 6.5∗zmlab . contour3d ( x , y , z , t )mlab . o u t l i n e ( )mlab . co lo rba r ( )

Simple solution

l a t = l inspace (−89, 89 , 37)lon = l inspace (0 , 360 , 37)z = l inspace (0 , 100 , 11)

x , y , z = mgrid [0 :360 :37 j , −89:89:37 j ,0:100:11 j ]

t = 288.15 − 6.5∗zmlab . contour3d ( x , y , z , t )mlab . o u t l i n e ( )mlab . co lo rba r ( )

What happens underneath?

P = mlab . p i p e l i n esrc = P. s c a l a r _ f i e l d ( x , y , z , t )i so = P. iso_sur face ( src )# Try t h i s .pr in t src

The underlying datasetfrom enthought . t v t k . ap i import t v t ko 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 =or ig ,

spacing=spacing ,dimensions=dims )

i d . po in t_data . sca la rs = t . T . f l a t t e n ( )i d . po in t_data . sca la rs . name = ’T ’# View i t .src = P. add_dataset ( i d )i so = P. iso_sur face ( src )

The general ideaSpecify the points (explicitly or implicitly)Specify the connectivity between the points(explicit/implicit)The connectivity lets you build “cells” that breakthe space into piecesSpecify “attribute” data at the points or cells

Cell data

Points Rectangular cell

Triangular cells Point data

Types of datasets

Implicit topology (structured):Image data (structured points)Rectilinear gridsStructured grids

Explicit topology (unstructured):Polygonal data (surfaces)Unstructured grids

Implicit versus explicit topology

Implicit topology associated with points:The X co-ordinate increases first, Y next and Z last

Easiest example: a rectangular meshNon-rectangular mesh certainly possible

On a sphere?lon , l a t , h t = x∗ p i /180 , (90+y )∗ p i /180 , zr = (1+0.005∗ ht )tmp = r ∗ s in ( l a t )# Poin ts on the spherex , y , z = tmp∗cos ( lon ) , tmp∗ s in ( lon ) , r ∗cos ( l a t )p ts = empty ( x . shape + ( 3 , ) , dtype= f l o a t )p ts [ . . . , 0 ] = xpts [ . . . , 1 ] = ypts [ . . . , 2 ] = z

# Reorder the po in t s / sca la rs f o r VTKpts = pts . t ranspose (2 , 1 , 0 , 3 ) . copy ( )p ts . shape = pts . s i ze /3 , 3t = t . T . copy ( )

sg = t v t k . S t ruc tu redGr id ( )sg . dimensions = x . shapesg . po in t s = ptssg . po in t_data . sca la rs = t . r ave l ( )sg . po in t_data . sca la rs . name = ’T ’

P = mlab . p i p e l i n esrc = P. add_dataset ( sg )P . gr id_p lane ( src )P . i so_sur face ( src , contours =1)

mlab . show ( )

# Save a dataset to d isk .from enthought . t v t k . ap i import wr i te_da tawr i te_da ta ( dataset , fname )

# Open back the data .mlab . p i p e l i n e . open ( fname )

Try right clicking a node!

Unstructured grids

Explicit topology specificationSpecified via connectivity listsDifferent number of neighbors, different types ofcells

PolyDatafrom enthought . t v t k . ap i import t v t k# The po in t s i n 3D.po in t s = ar ray ( [ [ 0 , 0 , 0 ] , [ 1 , 0 , 0 ] , [ 0 , 1 , 0 ] , [ 0 , 0 , 1 ] ] , ’ f ’ )# Connec t i v i t y v ia i nd i ces to the po in t s .t r i a n g l e s = ar ray ( [ [ 0 , 1 , 3 ] , [ 0 , 3 , 2 ] , [ 1 , 2 , 3 ] , [ 0 , 2 , 1 ] ] )# Creat ing the data ob jec t .

mesh = t v t k . PolyData ( )mesh . po in t s = po in t s # the po in t smesh . 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 / ve r t s use : mesh . l i n e s = l i n e s ; mesh . ve r t s = v e r t i c e s# Now create some po in t data .temperature = ar ray ( [ 1 0 , 20 ,20 , 30 ] , ’ f ’ )mesh . po in t_data . sca la rs = temperaturemesh . po in t_data . sca la rs . name = ’ temperature ’

PolyDatafrom enthought . t v t k . ap i import t v t k# The po in t s i n 3D.po in t s = ar ray ( [ [ 0 , 0 , 0 ] , [ 1 , 0 , 0 ] , [ 0 , 1 , 0 ] , [ 0 , 0 , 1 ] ] , ’ f ’ )# Connec t i v i t y v ia i nd i ces to the po in t s .t r i a n g l e s = ar ray ( [ [ 0 , 1 , 3 ] , [ 0 , 3 , 2 ] , [ 1 , 2 , 3 ] , [ 0 , 2 , 1 ] ] )# Creat ing the data ob jec t .

mesh = t v t k . PolyData ( )mesh . po in t s = po in t s # the po in t smesh . 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 / ve r t s use : mesh . l i n e s = l i n e s ; mesh . ve r t s = v e r t i c e s# Now create some po in t data .temperature = ar ray ( [ 1 0 , 20 ,20 , 30 ] , ’ f ’ )mesh . po in t_data . sca la rs = temperaturemesh . po in t_data . sca la rs . name = ’ temperature ’

Summary

Advanced features

Command line arguments, timeseries,scripting

A demo with files

$ mayavi2 −h

$ mayavi2 −d boundary . xml −m Surface \−d f l u i d _ 0 . xml −m Surface

Thank you!

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